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| Meta Title | sin(2pi)cos(pi) |
| Meta Description | Detailed step by step solution for sin(2pi)cos(pi) |
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| Boilerpipe Text | Solution
Solution
Solution steps
Rewrite using trig identities:
Rewrite
as
Apply the periodicity of
:
Use the following trivial identity:
periodicity table with
cycle:
Use the following trivial identity:
periodicity table with
cycle:
Simplify
Popular Examples
-5cot(pi/2)
(92)/(tan(12))
-2cos(-pi/4)
(cos(50))/(cos(30))
(1+cos(20)-sin(20))/(1-cos(20)-sin(20))
Frequently Asked Questions (FAQ)
What is the value of sin(2pi)cos(pi) ?
The value of sin(2pi)cos(pi) is 0 |
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# sin(2pi)cos(pi)
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## Solution
sin(2ฯ)cos(ฯ)
## Solution
0
Hide Steps
Solution steps
sin(2ฯ)cos(ฯ)
Rewrite using trig identities:sin(2ฯ)\=0
sin(2ฯ)
sin(2ฯ)\=sin(0)
sin(2ฯ)
Rewrite 2ฯ as 2ฯ\+0\=sin(2ฯ\+0)
Apply the periodicity of sin: sin(x\+2ฯ)\=sin(x)sin(2ฯ\+0)\=sin(0)\=sin(0)
\=sin(0)
Use the following trivial identity:sin(0)\=0
sin(0)
sin(x) periodicity table with 2ฯn cycle:
x06ฯโ4ฯโ3ฯโ2ฯโ32ฯโ43ฯโ65ฯโโ
sin(x)021โ
2
2
โ
โ
2
3
โ
โ
1
2
3
โ
โ
2
2
โ
โ
21โ
โ
xฯ67ฯโ45ฯโ34ฯโ23ฯโ35ฯโ47ฯโ611ฯโโ
sin(x)0โ21โ
โ
2
2
โ
โ
โ
2
3
โ
โ
โ1
โ
2
3
โ
โ
โ
2
2
โ
โ
โ21โ
โ
โ
\=0
\=0
Use the following trivial identity:cos(ฯ)\=(โ1)
cos(ฯ)
cos(x) periodicity table with 2ฯn cycle:
x06ฯโ4ฯโ3ฯโ2ฯโ32ฯโ43ฯโ65ฯโโ
cos(x)1
2
3
โ
โ
2
2
โ
โ
21โ0โ21โ
โ
2
2
โ
โ
โ
2
3
โ
โ
โ
xฯ67ฯโ45ฯโ34ฯโ23ฯโ35ฯโ47ฯโ611ฯโโ
cos(x)โ1
โ
2
3
โ
โ
โ
2
2
โ
โ
โ21โ021โ
2
2
โ
โ
2
3
โ
โ
โ
โ
\=(โ1)
\=0โ
(โ1)
Simplify\=0
Enter your problem
## Popular Examples
[\-5cot(pi/2)](https://www.symbolab.com/popular-trigonometry/trigonometry-37573)[โ5cot(2ฯโ)](https://www.symbolab.com/popular-trigonometry/trigonometry-37573)[(92)/(tan(12))](https://www.symbolab.com/popular-trigonometry/trigonometry-37575)[tan(12โ)92โ](https://www.symbolab.com/popular-trigonometry/trigonometry-37575)[\-2cos(-pi/4)](https://www.symbolab.com/popular-trigonometry/trigonometry-37576)[โ2cos(โ4ฯโ)](https://www.symbolab.com/popular-trigonometry/trigonometry-37576)[(cos(50))/(cos(30))](https://www.symbolab.com/popular-trigonometry/trigonometry-37577)[cos(30โ)cos(50โ)โ](https://www.symbolab.com/popular-trigonometry/trigonometry-37577)[(1+cos(20)-sin(20))/(1-cos(20)-sin(20))](https://www.symbolab.com/popular-trigonometry/trigonometry-37579)[1โcos(20โ)โsin(20โ)1\+cos(20โ)โsin(20โ)โ](https://www.symbolab.com/popular-trigonometry/trigonometry-37579)
## Frequently Asked Questions (FAQ)
- ### What is the value of sin(2pi)cos(pi) ?
The value of sin(2pi)cos(pi) is 0
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| Readable Markdown | ## Solution
## Solution
Solution steps
Rewrite using trig identities:
Rewrite as
Apply the periodicity of :
Use the following trivial identity:
periodicity table with cycle:
Use the following trivial identity:
periodicity table with cycle:
Simplify
## Popular Examples
[\-5cot(pi/2)](https://www.symbolab.com/popular-trigonometry/trigonometry-37573)[(92)/(tan(12))](https://www.symbolab.com/popular-trigonometry/trigonometry-37575)[\-2cos(-pi/4)](https://www.symbolab.com/popular-trigonometry/trigonometry-37576)[(cos(50))/(cos(30))](https://www.symbolab.com/popular-trigonometry/trigonometry-37577)[(1+cos(20)-sin(20))/(1-cos(20)-sin(20))](https://www.symbolab.com/popular-trigonometry/trigonometry-37579)
## Frequently Asked Questions (FAQ)
- ### What is the value of sin(2pi)cos(pi) ?
The value of sin(2pi)cos(pi) is 0 |
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