# Trigonometric problem

• Nov 11th 2012, 09:21 AM
sunrise
Trigonometric problem
Hello, I coldnt solve this problem

May you help me?

If y=sin(x)*cos(x) then what is the period?

I know Sin(x) and Cos(x) periods 2pi
Tan(x) and Cot(x) are pi but i dont know how i can solve?

Thanks
• Nov 11th 2012, 09:29 AM
skeeter
Re: Trigonometric problem
Quote:

Originally Posted by sunrise
Hello, I coldnt solve this problem

May you help me?

If y=sin(x)*cos(x) then what is the period?

I know Sin(x) and Cos(x) periods 2pi
Tan(x) and Cot(x) are pi but i dont know how i can solve?

Thanks

use the double angle identity for sine, note ...

$\displaystyle \sin{x}\cos{x} = \frac{1}{2}\sin(2x)$
• Nov 11th 2012, 09:43 AM
sunrise
Re: Trigonometric problem
So,
As I learned answer is pi

1\2*sin(2x) is equal to the pi? How i can show?

• Nov 11th 2012, 11:09 AM
skeeter
Re: Trigonometric problem
Quote:

Originally Posted by sunrise
So,
As I learned answer is pi

1\2*sin(2x) is equal to the pi?

you should know the period, $\displaystyle T$ , of $\displaystyle y = A\sin(Bx)$ is $\displaystyle T = \frac{2\pi}{B}$
• Nov 11th 2012, 11:17 AM
sunrise
Re: Trigonometric problem
Thank you