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1. Shard Calculation

Query:

Response:

Calculated Shard: 185 (from laksa086)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa185.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://www.cuemath.com/trigonometry/sin-2pi-3/\')), getAhrefsUnparsedNoserviceFromURL(\'https://www.cuemath.com/trigonometry/sin-2pi-3/\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/www.cuemath.com\/trigonometry\/sin-2pi-3\/","crawl_time":1776665308,"first_indexed_time":1639092320,"http_code":200,"src_unparsed":"com,cuemath!www,\/trigonometry\/sin-2pi-3\/ s443","src_root_hash":"6203651625873809585","history_drop_reason":null,"meta_title":"Sin 2pi\/3 - Find Value of Sin 2pi\/3 | Sin 2π\/3","meta_descriptions":["Sin 2pi\/3 degrees is the value of sine trigonometric function for an angle equal to 2pi\/3. Understand methods to find the value of sin 2pi\/3 with examples and FAQs."],"attrs_boilerpipe_text":"The value of\nsin 2pi\/3 is 0.8660254. . .\n. Sin 2pi\/3 radians in degrees is written as sin ((2π\/3) × 180°\/π), i.e., sin (120°). In this article, we will discuss the methods to find the value of sin 2pi\/3 with examples.\nSin 2pi\/3:\n√3\/2\nSin 2pi\/3 in decimal:\n0.8660254. . .\nSin (-2pi\/3):\n-0.8660254. . . or -(√3\/2)\nSin 2pi\/3 in degrees:\nsin (120°)\nWhat is the Value of Sin 2pi\/3?\nThe value of sin 2pi\/3 in\ndecimal\nis 0.866025403. . .. Sin 2pi\/3 can also be expressed using the equivalent of the given\nangle\n(2pi\/3) in degrees (120°).\nWe know, using\nradian to degree\nconversion, θ in degrees = θ in radians × (180°\/\npi\n)\n⇒ 2pi\/3 radians = 2pi\/3 × (180°\/pi) = 120° or 120\ndegrees\n∴ sin 2pi\/3 = sin 2π\/3 = sin(120°) = √3\/2 or 0.8660254. . .\nExplanation:\nFor sin 2pi\/3, the angle 2pi\/3 lies between pi\/2 and pi (Second\nQuadrant\n). Since sine function is positive in the second quadrant, thus sin 2pi\/3 value = √3\/2 or 0.8660254. . .\nSince the sine function is a\nperiodic function\n, we can represent sin 2pi\/3 as, sin 2pi\/3 = sin(2pi\/3 + n × 2pi), n ∈ Z.\n⇒ sin 2pi\/3 = sin 8pi\/3 = sin 14pi\/3 , and so on.\nNote:\nSince, sine is an\nodd function\n, the value of sin(-2pi\/3) = -sin(2pi\/3).\nMethods to Find Value of Sin 2pi\/3\nThe sine function is positive in the 2nd quadrant. The value of sin 2pi\/3 is given as 0.86602. . .. We can find the value of sin 2pi\/3 by:\nUsing Unit Circle\nUsing Trigonometric Functions\nSin 2pi\/3 Using Unit Circle\nTo find the value of sin 2π\/3 using the unit circle:\nRotate ‘r’ anticlockwise to form 2pi\/3 angle with the positive x-axis.\nThe sin of 2pi\/3 equals the y-coordinate(0.866) of the point of intersection (-0.5, 0.866) of unit circle and r.\nHence the value of sin 2pi\/3 = y = 0.866 (approx)\nSin 2pi\/3 in Terms of Trigonometric Functions\nUsing\ntrigonometry\nformulas, we can represent the sin 2pi\/3 as:\n± √(1-cos²(2pi\/3))\n± tan(2pi\/3)\/√(1 + tan²(2pi\/3))\n± 1\/√(1 + cot²(2pi\/3))\n± √(sec²(2pi\/3) - 1)\/sec(2pi\/3)\n1\/cosec(2pi\/3)\nNote:\nSince 2pi\/3 lies in the 2nd Quadrant, the final value of sin 2pi\/3 will be positive.\nWe can use trigonometric identities to represent sin 2pi\/3 as,\nsin(pi - 2pi\/3) = sin pi\/3\n-sin(pi + 2pi\/3) = -sin 5pi\/3\ncos(pi\/2 - 2pi\/3) = cos(-pi\/6)\n-cos(pi\/2 + 2pi\/3) = -cos 7pi\/6\n☛ Also Check:\ntan 3pi\/2\nsin pi\/3\ncos 17pi\/12\ntan 2pi\/3\nsec pi\/3\nsin 3pi\/2\nFAQs on Sin 2pi\/3\nWhat is Sin 2pi\/3?\nSin 2pi\/3 is the value of sine\ntrigonometric function\nfor an angle equal to 2pi\/3 radians.\nThe value of sin 2pi\/3 is √3\/2 or 0.866 (approx).\nWhat is the Value of Sin 2pi\/3 in Terms of Cosec 2pi\/3?\nSince the\ncosecant function\nis the reciprocal of the\nsine function\n, we can write sin 2pi\/3 as 1\/cosec(2pi\/3). The value of cosec 2pi\/3 is equal to 1.15470.\nHow to Find Sin 2pi\/3 in Terms of Other Trigonometric Functions?\nUsing\ntrigonometry formula\n, the value of sin 2π\/3 can be given in terms of other trigonometric functions as:\n± √(1-cos²(2pi\/3))\n± tan(2pi\/3)\/√(1 + tan²(2pi\/3))\n± 1\/√(1 + cot²(2pi\/3))\n± √(sec²(2pi\/3) - 1)\/sec(2pi\/3)\n1\/cosec(2pi\/3)\n☛ Also check:\ntrigonometric table\nHow to Find the Value of Sin 2pi\/3?\nThe value of sin 2pi\/3 can be calculated by constructing an\nangle\nof 2π\/3\nradians\nwith the\nx-axis\n, and then finding the coordinates of the corresponding point (-0.5, 0.866) on the\nunit circle\n. The value of sin 2pi\/3 is equal to the y-coordinate (0.866). ∴ sin 2pi\/3 = 0.866.\nWhat is the Value of Sin 2pi\/3 in Terms of Tan 2pi\/3?\nWe know, using\ntrig identities\n, we can write sin 2pi\/3 as -tan(2pi\/3)\/√(1 + tan²(2pi\/3)). Here, the value of tan 2pi\/3 is equal to -1.732050.","attrs_markdown":"[Math Tutoring](https:\/\/www.cuemath.com\/math-online-classes)\n\n[Elementary K-2](https:\/\/www.cuemath.com\/math-online-classes\/grade-k-2)\n\n[Kindergarten](https:\/\/www.cuemath.com\/math-online-classes\/kindergarten)\n\n[Grade 1](https:\/\/www.cuemath.com\/math-online-classes\/grade-1)\n\n[Grade 2](https:\/\/www.cuemath.com\/math-online-classes\/grade-2)\n\n[Elementary 3-5](https:\/\/www.cuemath.com\/math-online-classes\/grade-3-5)\n\n[Grade 3](https:\/\/www.cuemath.com\/math-online-classes\/grade-3)\n\n[Grade 4](https:\/\/www.cuemath.com\/math-online-classes\/grade-4)\n\n[Grade 5](https:\/\/www.cuemath.com\/math-online-classes\/grade-5)\n\n[Middle School](https:\/\/www.cuemath.com\/math-online-classes\/grade-6-8)\n\n[Grade 6](https:\/\/www.cuemath.com\/math-online-classes\/grade-6)\n\n[Grade 7](https:\/\/www.cuemath.com\/math-online-classes\/grade-7)\n\n[Grade 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Prep](https:\/\/www.cuemath.com\/math-online-classes\/test-prep)\n\n[STAAR](https:\/\/www.cuemath.com\/test\/staar-test)\n\n[NJSLA](https:\/\/www.cuemath.com\/test\/njsla-test)\n\n[MAP](https:\/\/www.cuemath.com\/test\/map-test)\n\n[Math Kangaroo](https:\/\/www.cuemath.com\/test\/math-kangaroo)\n\n[CogAT](https:\/\/www.cuemath.com\/test\/cogat-test)\n\n[AASA](https:\/\/www.cuemath.com\/test\/aasa-test)\n\n[SBAC](https:\/\/www.cuemath.com\/test\/sbac-test)\n\n[AMC 8](https:\/\/www.cuemath.com\/test\/amc-8-test)\n\n[GMAS](https:\/\/www.cuemath.com\/test\/gmas-test)\n\n[IAR](https:\/\/www.cuemath.com\/test\/iar-test)\n\n[SSAT](https:\/\/www.cuemath.com\/test\/ssat-test)\n\n[Pricing](https:\/\/www.cuemath.com\/pricing)\n\nResources\n\n[MathFit Evaluation](https:\/\/www.cuemath.com\/mathfit-evaluation)\n\n[Math Test](https:\/\/www.cuemath.com\/math-test)\n\n[Events](https:\/\/www.cuemath.com\/events)\n\n[Blogs](https:\/\/www.cuemath.com\/blog)\n\n[Cuemath App](https:\/\/www.cuemath.com\/apps\/cuemath?utm_source=website_navbar)\n\nAbout Us\n\n[Our Impact](https:\/\/www.cuemath.com\/our-impact)\n\n[Our Tutors](https:\/\/www.cuemath.com\/our-tutors)\n\n[Our Story & Mission](https:\/\/www.cuemath.com\/about-us)\n\n[Our Reviews](https:\/\/www.cuemath.com\/our-reviews)\n\n[Cuemath Vs Others](https:\/\/www.cuemath.com\/blog\/tag\/cuemath-vs-others)\n\n[What is MathFit](https:\/\/www.cuemath.com\/blog\/what-does-it-mean-to-be-mathfit)\n\n[FAQs](https:\/\/www.cuemath.com\/frequently-asked-questions)\n\n[Learn]()[Practice]()[Download]()\n\n# Sin 2pi\/3\nThe value of **sin 2pi\/3 is 0.8660254. . .**. Sin 2pi\/3 radians in degrees is written as sin ((2π\/3) × 180°\/π), i.e., sin (120°). In this article, we will discuss the methods to find the value of sin 2pi\/3 with examples.\n\n- **Sin 2pi\/3:** √3\/2\n- **Sin 2pi\/3 in decimal:** 0.8660254. . .\n- **Sin (-2pi\/3):** -0.8660254. . . or -(√3\/2)\n- **Sin 2pi\/3 in degrees:**  sin (120°)\n## What is the Value of Sin 2pi\/3?\nThe value of sin 2pi\/3 in [decimal](https:\/\/www.cuemath.com\/numbers\/decimals\/) is 0.866025403. . .. Sin 2pi\/3 can also be expressed using the equivalent of the given [angle](https:\/\/www.cuemath.com\/geometry\/angles\/) (2pi\/3) in degrees (120°).\n\nWe know, using [radian to degree](https:\/\/www.cuemath.com\/geometry\/radians-to-degrees\/) conversion, θ in degrees = θ in radians × (180°\/[pi](https:\/\/www.cuemath.com\/geometry\/what-is-pi\/))  \n ⇒ 2pi\/3 radians = 2pi\/3 × (180°\/pi) = 120° or 120 [degrees](https:\/\/www.cuemath.com\/geometry\/degrees\/)  \n ∴ sin 2pi\/3 = sin 2π\/3 = sin(120°) = √3\/2 or 0.8660254. . .\n\n![Sin 2pi\/3](https:\/\/static.qumath.in\/static\/website\/old-cdn-static\/trigonometry\/sin-2-pi-3.png)\n\n**Explanation:**\n\nFor sin 2pi\/3, the angle 2pi\/3 lies between pi\/2 and pi (Second [Quadrant](https:\/\/www.cuemath.com\/geometry\/quadrant\/)). Since sine function is positive in the second quadrant, thus sin 2pi\/3 value = √3\/2 or 0.8660254. . .  \n Since the sine function is a [periodic function](https:\/\/www.cuemath.com\/algebra\/periodic-function\/), we can represent sin 2pi\/3 as, sin 2pi\/3 = sin(2pi\/3 + n × 2pi), n ∈ Z.  \n ⇒ sin 2pi\/3 = sin 8pi\/3 = sin 14pi\/3 , and so on.  \n **Note:** Since, sine is an [odd function](https:\/\/www.cuemath.com\/calculus\/odd-functions\/), the value of sin(-2pi\/3) = -sin(2pi\/3).\n\n## Methods to Find Value of Sin 2pi\/3\nThe sine function is positive in the 2nd quadrant. The value of sin 2pi\/3 is given as 0.86602. . .. We can find the value of sin 2pi\/3 by:\n\n- Using Unit Circle\n- Using Trigonometric Functions\n## Sin 2pi\/3 Using Unit Circle\n![value of sin 2pi\/3](https:\/\/static.qumath.in\/static\/website\/old-cdn-static\/trigonometry\/value-of-sin-2-pi-3.png)\n\nTo find the value of sin 2π\/3 using the unit circle:\n\n- Rotate ‘r’ anticlockwise to form 2pi\/3 angle with the positive x-axis.\n- The sin of 2pi\/3 equals the y-coordinate(0.866) of the point of intersection (-0.5, 0.866) of unit circle and r.\n\nHence the value of sin 2pi\/3 = y = 0.866 (approx)\n\n## Sin 2pi\/3 in Terms of Trigonometric Functions\nUsing [trigonometry](https:\/\/www.cuemath.com\/trigonometry\/) formulas, we can represent the sin 2pi\/3 as:\n\n- ± √(1-cos²(2pi\/3))\n- ± tan(2pi\/3)\/√(1 + tan²(2pi\/3))\n- ± 1\/√(1 + cot²(2pi\/3))\n- ± √(sec²(2pi\/3) - 1)\/sec(2pi\/3)\n- 1\/cosec(2pi\/3)\n\n**Note:** Since 2pi\/3 lies in the 2nd Quadrant, the final value of sin 2pi\/3 will be positive.\n\nWe can use trigonometric identities to represent sin 2pi\/3 as,\n\n- sin(pi - 2pi\/3) = sin pi\/3\n- \\-sin(pi + 2pi\/3) = -sin 5pi\/3\n- cos(pi\/2 - 2pi\/3) = cos(-pi\/6)\n- \\-cos(pi\/2 + 2pi\/3) = -cos 7pi\/6\n\n**☛ Also Check:**\n\n- [tan 3pi\/2](https:\/\/www.cuemath.com\/trigonometry\/tan-3pi-2\/)\n- [sin pi\/3](https:\/\/www.cuemath.com\/trigonometry\/sin-pi-3\/)\n- [cos 17pi\/12](https:\/\/www.cuemath.com\/trigonometry\/cos-17pi-12\/)\n- [tan 2pi\/3](https:\/\/www.cuemath.com\/trigonometry\/tan-2pi-3\/)\n- [sec pi\/3](https:\/\/www.cuemath.com\/trigonometry\/sec-pi-3\/)\n- [sin 3pi\/2](https:\/\/www.cuemath.com\/trigonometry\/sin-3pi-2\/)\n\n## Examples Using Sin 2pi\/3\n1. **Example 1: Using the value of sin 2pi\/3, solve: (1-cos²(2pi\/3)).**\n   \n   **Solution:**\n   \n   We know, (1-cos²(2pi\/3)) = (sin²(2pi\/3)) = 0.75  \n    ⇒ (1-cos²(2pi\/3)) = 0.75\n2. **Example 2: Simplify: 7 (sin(2pi\/3)\/sin(8pi\/3))**\n   \n   **Solution:**\n   \n   We know sin 2pi\/3 = sin 8pi\/3  \n    ⇒ 7 sin(2pi\/3)\/sin(8pi\/3) = 7(sin(2pi\/3)\/sin(2pi\/3))  \n    = 7(1) = 7\n3. **Example 3: Find the value of 5 sin(2pi\/3)\/7 cos(-pi\/6).**\n   \n   **Solution:**\n   \n   Using trigonometric identities, we know, sin(2pi\/3) = cos(pi\/2 - 2pi\/3) = cos(-pi\/6).  \n    ⇒ sin(2pi\/3) = cos(-pi\/6)  \n    ⇒ Value of 5 sin(2pi\/3)\/7 cos(-pi\/6) = 5\/7\n\nShow Solution \\>\n\n[go to slide](https:\/\/www.cuemath.com\/trigonometry\/sin-2pi-3\/#slide-913)[go to slide](https:\/\/www.cuemath.com\/trigonometry\/sin-2pi-3\/#slide-493)[go to slide](https:\/\/www.cuemath.com\/trigonometry\/sin-2pi-3\/#slide-999)\n\n![](https:\/\/d138zd1ktt9iqe.cloudfront.net\/media\/seo_landing_files\/topics-marketing-image-1612964508.png)\n\nReady to see the world through math’s eyes?\n\nMath is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.\n\n[Book a Free Trial Class](https:\/\/www.cuemath.com\/parent\/signup\/)\n\n## FAQs on Sin 2pi\/3\n### What is Sin 2pi\/3?\nSin 2pi\/3 is the value of sine [trigonometric function](https:\/\/www.cuemath.com\/trigonometry\/trigonometric-functions\/) for an angle equal to 2pi\/3 radians.  ***The value of sin 2pi\/3 is √3\/2 or 0.866 (approx).***\n\n### What is the Value of Sin 2pi\/3 in Terms of Cosec 2pi\/3?\nSince the [cosecant function](https:\/\/www.cuemath.com\/trigonometry\/cosecant-functions\/) is the reciprocal of the [sine function](https:\/\/www.cuemath.com\/trigonometry\/sine-function\/), we can write sin 2pi\/3 as 1\/cosec(2pi\/3). The value of cosec 2pi\/3 is equal to 1.15470.\n\n### How to Find Sin 2pi\/3 in Terms of Other Trigonometric Functions?\nUsing [trigonometry formula](https:\/\/www.cuemath.com\/trigonometry\/trigonometry-formula\/), the value of sin 2π\/3 can be given in terms of other trigonometric functions as:\n\n- ± √(1-cos²(2pi\/3))\n- ± tan(2pi\/3)\/√(1 + tan²(2pi\/3))\n- ± 1\/√(1 + cot²(2pi\/3))\n- ± √(sec²(2pi\/3) - 1)\/sec(2pi\/3)\n- 1\/cosec(2pi\/3)\n\n☛ Also check: [trigonometric table](https:\/\/www.cuemath.com\/trigonometry\/trigonometric-table\/)\n\n### How to Find the Value of Sin 2pi\/3?\nThe value of sin 2pi\/3 can be calculated by constructing an [angle](https:\/\/www.cuemath.com\/geometry\/angles\/) of 2π\/3 [radians](https:\/\/www.cuemath.com\/trigonometry\/what-is-a-radian\/) with the [x-axis](https:\/\/www.cuemath.com\/geometry\/x-and-y-axis\/), and then finding the coordinates of the corresponding point (-0.5, 0.866) on the [unit circle](https:\/\/www.cuemath.com\/geometry\/unit-circle\/). The value of sin 2pi\/3 is equal to the y-coordinate (0.866). ∴ sin 2pi\/3 = 0.866.\n\n### What is the Value of Sin 2pi\/3 in Terms of Tan 2pi\/3?\nWe know, using [trig identities](https:\/\/www.cuemath.com\/trigonometry\/trigonometric-identities\/), we can write sin 2pi\/3 as -tan(2pi\/3)\/√(1 + tan²(2pi\/3)). 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Sin 2pi\/3 radians in degrees is written as sin ((2π\/3) × 180°\/π), i.e., sin (120°). In this article, we will discuss the methods to find the value of sin 2pi\/3 with examples.\n\n- **Sin 2pi\/3:** √3\/2\n- **Sin 2pi\/3 in decimal:** 0.8660254. . .\n- **Sin (-2pi\/3):** -0.8660254. . . or -(√3\/2)\n- **Sin 2pi\/3 in degrees:**  sin (120°)\n## What is the Value of Sin 2pi\/3?\nThe value of sin 2pi\/3 in [decimal](https:\/\/www.cuemath.com\/numbers\/decimals\/) is 0.866025403. . .. Sin 2pi\/3 can also be expressed using the equivalent of the given [angle](https:\/\/www.cuemath.com\/geometry\/angles\/) (2pi\/3) in degrees (120°).\n\nWe know, using [radian to degree](https:\/\/www.cuemath.com\/geometry\/radians-to-degrees\/) conversion, θ in degrees = θ in radians × (180°\/[pi](https:\/\/www.cuemath.com\/geometry\/what-is-pi\/))  \n ⇒ 2pi\/3 radians = 2pi\/3 × (180°\/pi) = 120° or 120 [degrees](https:\/\/www.cuemath.com\/geometry\/degrees\/)  \n ∴ sin 2pi\/3 = sin 2π\/3 = sin(120°) = √3\/2 or 0.8660254. . .\n\n![Sin 2pi\/3](https:\/\/static.qumath.in\/static\/website\/old-cdn-static\/trigonometry\/sin-2-pi-3.png)\n\n**Explanation:**\n\nFor sin 2pi\/3, the angle 2pi\/3 lies between pi\/2 and pi (Second [Quadrant](https:\/\/www.cuemath.com\/geometry\/quadrant\/)). Since sine function is positive in the second quadrant, thus sin 2pi\/3 value = √3\/2 or 0.8660254. . .  \n Since the sine function is a [periodic function](https:\/\/www.cuemath.com\/algebra\/periodic-function\/), we can represent sin 2pi\/3 as, sin 2pi\/3 = sin(2pi\/3 + n × 2pi), n ∈ Z.  \n ⇒ sin 2pi\/3 = sin 8pi\/3 = sin 14pi\/3 , and so on.  \n **Note:** Since, sine is an [odd function](https:\/\/www.cuemath.com\/calculus\/odd-functions\/), the value of sin(-2pi\/3) = -sin(2pi\/3).\n\n## Methods to Find Value of Sin 2pi\/3\nThe sine function is positive in the 2nd quadrant. The value of sin 2pi\/3 is given as 0.86602. . .. We can find the value of sin 2pi\/3 by:\n\n- Using Unit Circle\n- Using Trigonometric Functions\n## Sin 2pi\/3 Using Unit Circle\n![value of sin 2pi\/3](https:\/\/static.qumath.in\/static\/website\/old-cdn-static\/trigonometry\/value-of-sin-2-pi-3.png)\n\nTo find the value of sin 2π\/3 using the unit circle:\n\n- Rotate ‘r’ anticlockwise to form 2pi\/3 angle with the positive x-axis.\n- The sin of 2pi\/3 equals the y-coordinate(0.866) of the point of intersection (-0.5, 0.866) of unit circle and r.\n\nHence the value of sin 2pi\/3 = y = 0.866 (approx)\n\n## Sin 2pi\/3 in Terms of Trigonometric Functions\nUsing [trigonometry](https:\/\/www.cuemath.com\/trigonometry\/) formulas, we can represent the sin 2pi\/3 as:\n\n- ± √(1-cos²(2pi\/3))\n- ± tan(2pi\/3)\/√(1 + tan²(2pi\/3))\n- ± 1\/√(1 + cot²(2pi\/3))\n- ± √(sec²(2pi\/3) - 1)\/sec(2pi\/3)\n- 1\/cosec(2pi\/3)\n\n**Note:** Since 2pi\/3 lies in the 2nd Quadrant, the final value of sin 2pi\/3 will be positive.\n\nWe can use trigonometric identities to represent sin 2pi\/3 as,\n\n- sin(pi - 2pi\/3) = sin pi\/3\n- \\-sin(pi + 2pi\/3) = -sin 5pi\/3\n- cos(pi\/2 - 2pi\/3) = cos(-pi\/6)\n- \\-cos(pi\/2 + 2pi\/3) = -cos 7pi\/6\n\n**☛ Also Check:**\n\n- [tan 3pi\/2](https:\/\/www.cuemath.com\/trigonometry\/tan-3pi-2\/)\n- [sin pi\/3](https:\/\/www.cuemath.com\/trigonometry\/sin-pi-3\/)\n- [cos 17pi\/12](https:\/\/www.cuemath.com\/trigonometry\/cos-17pi-12\/)\n- [tan 2pi\/3](https:\/\/www.cuemath.com\/trigonometry\/tan-2pi-3\/)\n- [sec pi\/3](https:\/\/www.cuemath.com\/trigonometry\/sec-pi-3\/)\n- [sin 3pi\/2](https:\/\/www.cuemath.com\/trigonometry\/sin-3pi-2\/)\n\n## FAQs on Sin 2pi\/3\n### What is Sin 2pi\/3?\nSin 2pi\/3 is the value of sine [trigonometric function](https:\/\/www.cuemath.com\/trigonometry\/trigonometric-functions\/) for an angle equal to 2pi\/3 radians.  ***The value of sin 2pi\/3 is √3\/2 or 0.866 (approx).***\n\n### What is the Value of Sin 2pi\/3 in Terms of Cosec 2pi\/3?\nSince the [cosecant function](https:\/\/www.cuemath.com\/trigonometry\/cosecant-functions\/) is the reciprocal of the [sine function](https:\/\/www.cuemath.com\/trigonometry\/sine-function\/), we can write sin 2pi\/3 as 1\/cosec(2pi\/3). The value of cosec 2pi\/3 is equal to 1.15470.\n\n### How to Find Sin 2pi\/3 in Terms of Other Trigonometric Functions?\nUsing [trigonometry formula](https:\/\/www.cuemath.com\/trigonometry\/trigonometry-formula\/), the value of sin 2π\/3 can be given in terms of other trigonometric functions as:\n\n- ± √(1-cos²(2pi\/3))\n- ± tan(2pi\/3)\/√(1 + tan²(2pi\/3))\n- ± 1\/√(1 + cot²(2pi\/3))\n- ± √(sec²(2pi\/3) - 1)\/sec(2pi\/3)\n- 1\/cosec(2pi\/3)\n\n☛ Also check: [trigonometric table](https:\/\/www.cuemath.com\/trigonometry\/trigonometric-table\/)\n\n### How to Find the Value of Sin 2pi\/3?\nThe value of sin 2pi\/3 can be calculated by constructing an [angle](https:\/\/www.cuemath.com\/geometry\/angles\/) of 2π\/3 [radians](https:\/\/www.cuemath.com\/trigonometry\/what-is-a-radian\/) with the [x-axis](https:\/\/www.cuemath.com\/geometry\/x-and-y-axis\/), and then finding the coordinates of the corresponding point (-0.5, 0.866) on the [unit circle](https:\/\/www.cuemath.com\/geometry\/unit-circle\/). The value of sin 2pi\/3 is equal to the y-coordinate (0.866). ∴ sin 2pi\/3 = 0.866.\n\n### What is the Value of Sin 2pi\/3 in Terms of Tan 2pi\/3?\nWe know, using [trig identities](https:\/\/www.cuemath.com\/trigonometry\/trigonometric-identities\/), we can write sin 2pi\/3 as -tan(2pi\/3)\/√(1 + tan²(2pi\/3)). Here, the value of tan 2pi\/3 is equal to -1.732050.","meta_canonical":null}

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Meta Title	Sin 2pi/3 - Find Value of Sin 2pi/3 \| Sin 2π/3
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Boilerpipe Text	The value of sin 2pi/3 is 0.8660254. . . . Sin 2pi/3 radians in degrees is written as sin ((2π/3) × 180°/π), i.e., sin (120°). In this article, we will discuss the methods to find the value of sin 2pi/3 with examples. Sin 2pi/3: √3/2 Sin 2pi/3 in decimal: 0.8660254. . . Sin (-2pi/3): -0.8660254. . . or -(√3/2) Sin 2pi/3 in degrees: sin (120°) What is the Value of Sin 2pi/3? The value of sin 2pi/3 in decimal is 0.866025403. . .. Sin 2pi/3 can also be expressed using the equivalent of the given angle (2pi/3) in degrees (120°). We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/ pi ) ⇒ 2pi/3 radians = 2pi/3 × (180°/pi) = 120° or 120 degrees ∴ sin 2pi/3 = sin 2π/3 = sin(120°) = √3/2 or 0.8660254. . . Explanation: For sin 2pi/3, the angle 2pi/3 lies between pi/2 and pi (Second Quadrant ). Since sine function is positive in the second quadrant, thus sin 2pi/3 value = √3/2 or 0.8660254. . . Since the sine function is a periodic function , we can represent sin 2pi/3 as, sin 2pi/3 = sin(2pi/3 + n × 2pi), n ∈ Z. ⇒ sin 2pi/3 = sin 8pi/3 = sin 14pi/3 , and so on. Note: Since, sine is an odd function , the value of sin(-2pi/3) = -sin(2pi/3). Methods to Find Value of Sin 2pi/3 The sine function is positive in the 2nd quadrant. The value of sin 2pi/3 is given as 0.86602. . .. We can find the value of sin 2pi/3 by: Using Unit Circle Using Trigonometric Functions Sin 2pi/3 Using Unit Circle To find the value of sin 2π/3 using the unit circle: Rotate ‘r’ anticlockwise to form 2pi/3 angle with the positive x-axis. The sin of 2pi/3 equals the y-coordinate(0.866) of the point of intersection (-0.5, 0.866) of unit circle and r. Hence the value of sin 2pi/3 = y = 0.866 (approx) Sin 2pi/3 in Terms of Trigonometric Functions Using trigonometry formulas, we can represent the sin 2pi/3 as: ± √(1-cos²(2pi/3)) ± tan(2pi/3)/√(1 + tan²(2pi/3)) ± 1/√(1 + cot²(2pi/3)) ± √(sec²(2pi/3) - 1)/sec(2pi/3) 1/cosec(2pi/3) Note: Since 2pi/3 lies in the 2nd Quadrant, the final value of sin 2pi/3 will be positive. We can use trigonometric identities to represent sin 2pi/3 as, sin(pi - 2pi/3) = sin pi/3 -sin(pi + 2pi/3) = -sin 5pi/3 cos(pi/2 - 2pi/3) = cos(-pi/6) -cos(pi/2 + 2pi/3) = -cos 7pi/6 ☛ Also Check: tan 3pi/2 sin pi/3 cos 17pi/12 tan 2pi/3 sec pi/3 sin 3pi/2 FAQs on Sin 2pi/3 What is Sin 2pi/3? Sin 2pi/3 is the value of sine trigonometric function for an angle equal to 2pi/3 radians. The value of sin 2pi/3 is √3/2 or 0.866 (approx). What is the Value of Sin 2pi/3 in Terms of Cosec 2pi/3? Since the cosecant function is the reciprocal of the sine function , we can write sin 2pi/3 as 1/cosec(2pi/3). The value of cosec 2pi/3 is equal to 1.15470. How to Find Sin 2pi/3 in Terms of Other Trigonometric Functions? Using trigonometry formula , the value of sin 2π/3 can be given in terms of other trigonometric functions as: ± √(1-cos²(2pi/3)) ± tan(2pi/3)/√(1 + tan²(2pi/3)) ± 1/√(1 + cot²(2pi/3)) ± √(sec²(2pi/3) - 1)/sec(2pi/3) 1/cosec(2pi/3) ☛ Also check: trigonometric table How to Find the Value of Sin 2pi/3? The value of sin 2pi/3 can be calculated by constructing an angle of 2π/3 radians with the x-axis , and then finding the coordinates of the corresponding point (-0.5, 0.866) on the unit circle . The value of sin 2pi/3 is equal to the y-coordinate (0.866). ∴ sin 2pi/3 = 0.866. What is the Value of Sin 2pi/3 in Terms of Tan 2pi/3? We know, using trig identities , we can write sin 2pi/3 as -tan(2pi/3)/√(1 + tan²(2pi/3)). Here, the value of tan 2pi/3 is equal to -1.732050.
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Sin 2pi/3 radians in degrees is written as sin ((2π/3) × 180°/π), i.e., sin (120°). In this article, we will discuss the methods to find the value of sin 2pi/3 with examples. - Sin 2pi/3: √3/2 - Sin 2pi/3 in decimal: 0.8660254. . . - Sin (-2pi/3): -0.8660254. . . or -(√3/2) - Sin 2pi/3 in degrees: sin (120°) ## What is the Value of Sin 2pi/3? The value of sin 2pi/3 in [decimal](https://www.cuemath.com/numbers/decimals/) is 0.866025403. . .. Sin 2pi/3 can also be expressed using the equivalent of the given [angle](https://www.cuemath.com/geometry/angles/) (2pi/3) in degrees (120°). We know, using [radian to degree](https://www.cuemath.com/geometry/radians-to-degrees/) conversion, θ in degrees = θ in radians × (180°/[pi](https://www.cuemath.com/geometry/what-is-pi/)) ⇒ 2pi/3 radians = 2pi/3 × (180°/pi) = 120° or 120 [degrees](https://www.cuemath.com/geometry/degrees/) ∴ sin 2pi/3 = sin 2π/3 = sin(120°) = √3/2 or 0.8660254. . . ![Sin 2pi/3](https://static.qumath.in/static/website/old-cdn-static/trigonometry/sin-2-pi-3.png) Explanation: For sin 2pi/3, the angle 2pi/3 lies between pi/2 and pi (Second [Quadrant](https://www.cuemath.com/geometry/quadrant/)). Since sine function is positive in the second quadrant, thus sin 2pi/3 value = √3/2 or 0.8660254. . . Since the sine function is a [periodic function](https://www.cuemath.com/algebra/periodic-function/), we can represent sin 2pi/3 as, sin 2pi/3 = sin(2pi/3 + n × 2pi), n ∈ Z. ⇒ sin 2pi/3 = sin 8pi/3 = sin 14pi/3 , and so on. Note: Since, sine is an [odd function](https://www.cuemath.com/calculus/odd-functions/), the value of sin(-2pi/3) = -sin(2pi/3). ## Methods to Find Value of Sin 2pi/3 The sine function is positive in the 2nd quadrant. The value of sin 2pi/3 is given as 0.86602. . .. We can find the value of sin 2pi/3 by: - Using Unit Circle - Using Trigonometric Functions ## Sin 2pi/3 Using Unit Circle ![value of sin 2pi/3](https://static.qumath.in/static/website/old-cdn-static/trigonometry/value-of-sin-2-pi-3.png) To find the value of sin 2π/3 using the unit circle: - Rotate ‘r’ anticlockwise to form 2pi/3 angle with the positive x-axis. - The sin of 2pi/3 equals the y-coordinate(0.866) of the point of intersection (-0.5, 0.866) of unit circle and r. Hence the value of sin 2pi/3 = y = 0.866 (approx) ## Sin 2pi/3 in Terms of Trigonometric Functions Using [trigonometry](https://www.cuemath.com/trigonometry/) formulas, we can represent the sin 2pi/3 as: - ± √(1-cos²(2pi/3)) - ± tan(2pi/3)/√(1 + tan²(2pi/3)) - ± 1/√(1 + cot²(2pi/3)) - ± √(sec²(2pi/3) - 1)/sec(2pi/3) - 1/cosec(2pi/3) Note: Since 2pi/3 lies in the 2nd Quadrant, the final value of sin 2pi/3 will be positive. We can use trigonometric identities to represent sin 2pi/3 as, - sin(pi - 2pi/3) = sin pi/3 - \-sin(pi + 2pi/3) = -sin 5pi/3 - cos(pi/2 - 2pi/3) = cos(-pi/6) - \-cos(pi/2 + 2pi/3) = -cos 7pi/6 ☛ Also Check: - [tan 3pi/2](https://www.cuemath.com/trigonometry/tan-3pi-2/) - [sin pi/3](https://www.cuemath.com/trigonometry/sin-pi-3/) - [cos 17pi/12](https://www.cuemath.com/trigonometry/cos-17pi-12/) - [tan 2pi/3](https://www.cuemath.com/trigonometry/tan-2pi-3/) - [sec pi/3](https://www.cuemath.com/trigonometry/sec-pi-3/) - [sin 3pi/2](https://www.cuemath.com/trigonometry/sin-3pi-2/) ## Examples Using Sin 2pi/3 1. Example 1: Using the value of sin 2pi/3, solve: (1-cos²(2pi/3)). Solution: We know, (1-cos²(2pi/3)) = (sin²(2pi/3)) = 0.75 ⇒ (1-cos²(2pi/3)) = 0.75 2. Example 2: Simplify: 7 (sin(2pi/3)/sin(8pi/3)) Solution: We know sin 2pi/3 = sin 8pi/3 ⇒ 7 sin(2pi/3)/sin(8pi/3) = 7(sin(2pi/3)/sin(2pi/3)) = 7(1) = 7 3. Example 3: Find the value of 5 sin(2pi/3)/7 cos(-pi/6). Solution: Using trigonometric identities, we know, sin(2pi/3) = cos(pi/2 - 2pi/3) = cos(-pi/6). ⇒ sin(2pi/3) = cos(-pi/6) ⇒ Value of 5 sin(2pi/3)/7 cos(-pi/6) = 5/7 Show Solution \> [go to slide](https://www.cuemath.com/trigonometry/sin-2pi-3/#slide-913)[go to slide](https://www.cuemath.com/trigonometry/sin-2pi-3/#slide-493)[go to slide](https://www.cuemath.com/trigonometry/sin-2pi-3/#slide-999) ![](https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/topics-marketing-image-1612964508.png) Ready to see the world through math’s eyes? Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything. [Book a Free Trial Class](https://www.cuemath.com/parent/signup/) ## FAQs on Sin 2pi/3 ### What is Sin 2pi/3? Sin 2pi/3 is the value of sine [trigonometric function](https://www.cuemath.com/trigonometry/trigonometric-functions/) for an angle equal to 2pi/3 radians. *The value of sin 2pi/3 is √3/2 or 0.866 (approx).* ### What is the Value of Sin 2pi/3 in Terms of Cosec 2pi/3? Since the [cosecant function](https://www.cuemath.com/trigonometry/cosecant-functions/) is the reciprocal of the [sine function](https://www.cuemath.com/trigonometry/sine-function/), we can write sin 2pi/3 as 1/cosec(2pi/3). The value of cosec 2pi/3 is equal to 1.15470. ### How to Find Sin 2pi/3 in Terms of Other Trigonometric Functions? Using [trigonometry formula](https://www.cuemath.com/trigonometry/trigonometry-formula/), the value of sin 2π/3 can be given in terms of other trigonometric functions as: - ± √(1-cos²(2pi/3)) - ± tan(2pi/3)/√(1 + tan²(2pi/3)) - ± 1/√(1 + cot²(2pi/3)) - ± √(sec²(2pi/3) - 1)/sec(2pi/3) - 1/cosec(2pi/3) ☛ Also check: [trigonometric table](https://www.cuemath.com/trigonometry/trigonometric-table/) ### How to Find the Value of Sin 2pi/3? The value of sin 2pi/3 can be calculated by constructing an [angle](https://www.cuemath.com/geometry/angles/) of 2π/3 [radians](https://www.cuemath.com/trigonometry/what-is-a-radian/) with the [x-axis](https://www.cuemath.com/geometry/x-and-y-axis/), and then finding the coordinates of the corresponding point (-0.5, 0.866) on the [unit circle](https://www.cuemath.com/geometry/unit-circle/). The value of sin 2pi/3 is equal to the y-coordinate (0.866). ∴ sin 2pi/3 = 0.866. ### What is the Value of Sin 2pi/3 in Terms of Tan 2pi/3? We know, using [trig identities](https://www.cuemath.com/trigonometry/trigonometric-identities/), we can write sin 2pi/3 as -tan(2pi/3)/√(1 + tan²(2pi/3)). Here, the value of tan 2pi/3 is equal to -1.732050. Explore math program Download FREE Study Materials Trigonometry Explore math program Math worksheets and visual curriculum Book a FREE Class Become MathFit™: Boost math skills with daily fun challenges and puzzles. Download the app STRATEGY GAMES LOGIC PUZZLES MENTAL MATH Become MathFit™: Boost math skills with daily fun challenges and puzzles. 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Readable Markdown	The value of sin 2pi/3 is 0.8660254. . .. Sin 2pi/3 radians in degrees is written as sin ((2π/3) × 180°/π), i.e., sin (120°). In this article, we will discuss the methods to find the value of sin 2pi/3 with examples. - Sin 2pi/3: √3/2 - Sin 2pi/3 in decimal: 0.8660254. . . - Sin (-2pi/3): -0.8660254. . . or -(√3/2) - Sin 2pi/3 in degrees: sin (120°) ## What is the Value of Sin 2pi/3? The value of sin 2pi/3 in [decimal](https://www.cuemath.com/numbers/decimals/) is 0.866025403. . .. Sin 2pi/3 can also be expressed using the equivalent of the given [angle](https://www.cuemath.com/geometry/angles/) (2pi/3) in degrees (120°). We know, using [radian to degree](https://www.cuemath.com/geometry/radians-to-degrees/) conversion, θ in degrees = θ in radians × (180°/[pi](https://www.cuemath.com/geometry/what-is-pi/)) ⇒ 2pi/3 radians = 2pi/3 × (180°/pi) = 120° or 120 [degrees](https://www.cuemath.com/geometry/degrees/) ∴ sin 2pi/3 = sin 2π/3 = sin(120°) = √3/2 or 0.8660254. . . ![Sin 2pi/3](https://static.qumath.in/static/website/old-cdn-static/trigonometry/sin-2-pi-3.png) Explanation: For sin 2pi/3, the angle 2pi/3 lies between pi/2 and pi (Second [Quadrant](https://www.cuemath.com/geometry/quadrant/)). Since sine function is positive in the second quadrant, thus sin 2pi/3 value = √3/2 or 0.8660254. . . Since the sine function is a [periodic function](https://www.cuemath.com/algebra/periodic-function/), we can represent sin 2pi/3 as, sin 2pi/3 = sin(2pi/3 + n × 2pi), n ∈ Z. ⇒ sin 2pi/3 = sin 8pi/3 = sin 14pi/3 , and so on. Note: Since, sine is an [odd function](https://www.cuemath.com/calculus/odd-functions/), the value of sin(-2pi/3) = -sin(2pi/3). ## Methods to Find Value of Sin 2pi/3 The sine function is positive in the 2nd quadrant. The value of sin 2pi/3 is given as 0.86602. . .. We can find the value of sin 2pi/3 by: - Using Unit Circle - Using Trigonometric Functions ## Sin 2pi/3 Using Unit Circle ![value of sin 2pi/3](https://static.qumath.in/static/website/old-cdn-static/trigonometry/value-of-sin-2-pi-3.png) To find the value of sin 2π/3 using the unit circle: - Rotate ‘r’ anticlockwise to form 2pi/3 angle with the positive x-axis. - The sin of 2pi/3 equals the y-coordinate(0.866) of the point of intersection (-0.5, 0.866) of unit circle and r. Hence the value of sin 2pi/3 = y = 0.866 (approx) ## Sin 2pi/3 in Terms of Trigonometric Functions Using [trigonometry](https://www.cuemath.com/trigonometry/) formulas, we can represent the sin 2pi/3 as: - ± √(1-cos²(2pi/3)) - ± tan(2pi/3)/√(1 + tan²(2pi/3)) - ± 1/√(1 + cot²(2pi/3)) - ± √(sec²(2pi/3) - 1)/sec(2pi/3) - 1/cosec(2pi/3) Note: Since 2pi/3 lies in the 2nd Quadrant, the final value of sin 2pi/3 will be positive. We can use trigonometric identities to represent sin 2pi/3 as, - sin(pi - 2pi/3) = sin pi/3 - \-sin(pi + 2pi/3) = -sin 5pi/3 - cos(pi/2 - 2pi/3) = cos(-pi/6) - \-cos(pi/2 + 2pi/3) = -cos 7pi/6 ☛ Also Check: - [tan 3pi/2](https://www.cuemath.com/trigonometry/tan-3pi-2/) - [sin pi/3](https://www.cuemath.com/trigonometry/sin-pi-3/) - [cos 17pi/12](https://www.cuemath.com/trigonometry/cos-17pi-12/) - [tan 2pi/3](https://www.cuemath.com/trigonometry/tan-2pi-3/) - [sec pi/3](https://www.cuemath.com/trigonometry/sec-pi-3/) - [sin 3pi/2](https://www.cuemath.com/trigonometry/sin-3pi-2/) ## FAQs on Sin 2pi/3 ### What is Sin 2pi/3? Sin 2pi/3 is the value of sine [trigonometric function](https://www.cuemath.com/trigonometry/trigonometric-functions/) for an angle equal to 2pi/3 radians. *The value of sin 2pi/3 is √3/2 or 0.866 (approx).* ### What is the Value of Sin 2pi/3 in Terms of Cosec 2pi/3? Since the [cosecant function](https://www.cuemath.com/trigonometry/cosecant-functions/) is the reciprocal of the [sine function](https://www.cuemath.com/trigonometry/sine-function/), we can write sin 2pi/3 as 1/cosec(2pi/3). The value of cosec 2pi/3 is equal to 1.15470. ### How to Find Sin 2pi/3 in Terms of Other Trigonometric Functions? Using [trigonometry formula](https://www.cuemath.com/trigonometry/trigonometry-formula/), the value of sin 2π/3 can be given in terms of other trigonometric functions as: - ± √(1-cos²(2pi/3)) - ± tan(2pi/3)/√(1 + tan²(2pi/3)) - ± 1/√(1 + cot²(2pi/3)) - ± √(sec²(2pi/3) - 1)/sec(2pi/3) - 1/cosec(2pi/3) ☛ Also check: [trigonometric table](https://www.cuemath.com/trigonometry/trigonometric-table/) ### How to Find the Value of Sin 2pi/3? The value of sin 2pi/3 can be calculated by constructing an [angle](https://www.cuemath.com/geometry/angles/) of 2π/3 [radians](https://www.cuemath.com/trigonometry/what-is-a-radian/) with the [x-axis](https://www.cuemath.com/geometry/x-and-y-axis/), and then finding the coordinates of the corresponding point (-0.5, 0.866) on the [unit circle](https://www.cuemath.com/geometry/unit-circle/). The value of sin 2pi/3 is equal to the y-coordinate (0.866). ∴ sin 2pi/3 = 0.866. ### What is the Value of Sin 2pi/3 in Terms of Tan 2pi/3? We know, using [trig identities](https://www.cuemath.com/trigonometry/trigonometric-identities/), we can write sin 2pi/3 as -tan(2pi/3)/√(1 + tan²(2pi/3)). Here, the value of tan 2pi/3 is equal to -1.732050.
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