trig identity

**smartcar29** · September 15th 2009, 08:41 AM

hi

have this function g(x)=cos(x)exp(2/3sin(x)) 0<x<2pie

also have derivative $g'(x)=1/3(2-3sinx-2sin^2x)$ (exp2/3sinx)

i need to find the stationary points of g(x) and classify each point min and max. the domain is [0,2pie]

my main problem is i do not know how to get any values to use in original function i am not sure about trig identity. i am sure that i need to set $1/3(2-3sinx-2sin^2x)$ to 0 but thats as far i as go.

any help would be great

**redsoxfan325** · September 15th 2009, 09:07 AM

Originally Posted by smartcar29

hi

have this function g(x)=cos(x)exp(2/3sin(x)) 0<x<2pie

also have derivative $g'(x)=1/3(2-3sinx-2sin^2x)$ (exp2/3sinx)

i need to find the stationary points of g(x) and classify each point min and max. the domain is [0,2pie]

my main problem is i do not know how to get any values to use in original function i am not sure about trig identity. i am sure that i need to set $1/3(2-3sinx-2sin^2x)$ to 0 but thats as far i as go.

any help would be great

Don't worry about the $\frac{1}{3}$ ; it's just a constant multiple. To solve $2-3\sin x-2\sin^2x=0$ , just treat $\sin x$ like you would $x$ and factor it.

We know that $2-3x-2x^2$ factors into $(1-2x)(2+x)$ , so $2-3\sin x-2\sin^2x$ factors into $(1-2\sin x)(2+\sin x)$ . Then set each part equal to 0.

Spoiler: