1. ## Random Trig Problems

Getting hung up on some trig-solving...

For the first problem here, we get 8x-2sec^2(x) when derived and then you set that equal to 0 to find the critical points. I have no clue at all how to solve that.

The second, you get -8sin(x)+4cos^2(x) when taking the derivative. Again, set it equal to 0 and then I'm stumped.

Feels bad that this is just algebra, but I dunno what to do. Will greatly appreciate any help!

2. ## Re: Random Trig Problems

solve for x: 8x=2sec^2 x - Wolfram|Alpha Results

http://m.wolframalpha.com/input/?i=s...x%3D4cos%5E2+x

These have no rational solutions. You need a computer algebra system to find critical points.

You could simplify the second one to:
$\displaystyle \sin^2 x+2\sin x-1=0 \Longrightarrow \sin x = -1\pm \sqrt{2}$

3. ## Re: Random Trig Problems

That helped for 9, still can't get 13, though.

4. ## Re: Random Trig Problems

That's because $\displaystyle \dfrac{d}{dx}(8\cos x+4\sin^2 x)=-8\sin x +8\sin x \cos x$

When you set that to zero, you get $\displaystyle \sin x (\cos x -1) =0$

So $\displaystyle x=-\pi , 0 ,\pi$