f(x)= sin2(wx) + squroot3sin(wx)sin(pi/2 + wx)    w>0 If the period of f(x) is pi, compute the solution of equation.  I've done problems similar to this, but this one is quite complicated. I don't know where to start. Any help would be greatly appreciated!

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Use `sin(pi/2 +wx) = sin(pi/2)*cos wx + sin wx*cos (pi/2)`

`sin(pi/2)=1; cos (pi/2)=0`

`sin(pi/2 +wx) = cos wx`

Use `sin 2(wx)=2 sin(wx)*cos (wx)`

`f(x) = 2 sin(wx)*cos (wx) + sqrt3*sin(wx)*cos (wx)`

`f(x) = sin(wx)*cos (wx)*(2 + sqrt 3)`

`` If `x = pi =gt f(x) = sin(wpi)*cos (wpi)*(2 + sqrt 3)=0, since sin wpi=0`

If `x=pi/2 =gt sin(wpi/2)*cos (wpi/2)*(2 + sqrt 3)=0, since cos (wpi/2) = 0`

Answer: If the period of the function is `pi` , then the value of the function is 0, therefore x=`pi ` is the solution of the equation of the function.

Approved by eNotes Editorial Team