Thread: Derivative of trig function to equal zero.

Hi, everyone,

I have the trig function g(x)=cos^4(x)-cos^2(x) and i have found g'(x) to be -4sin(x)cos^3(x)+2sin(x)cos(x). how would i find when the derivative is equal to zero? I started to rearrange it to see if that would help but now i am stuck.

2sin(x)cos(x)=sin(2x) and,

-4sin(x)cos^3(x)=-4((1/2)sin(2x))cos^2(x)=-2sin(2x)cos^2(x).

Any ideas?

Thanks

Hey mcleja.

Hint: Try dividing both sides by sin(2x) and simplify.

Put g’(x) = 0, we get
2cosx sinx – 4cos^3xsinx = 0
2cosx sinx [ 1 – 2 cos^2x] = 0
Cos x = 0 gives x = π/2 + nπ
Sinx = 0 gives x = nπ
[ 1 – 2 cos^2x] = 0 gives cos x = ±1/√2 that will give x = nπ ± π/4