finding angle between two curves using knowledge of derivative The curves $y=\sin 2x$ and $y=\cos 2x$ intersect at $x=\frac{π}{8}$.
Find angle between the curves at this point. Extend your solution to find the angle between the curves $y=\sin 5x$ and $y=\cos 5x$.
My solution: 
When $x = 0.3927$, $y= 0.7071$
$y'(\frac{π}{8})=0.707$ 
$\tan(a)=0.707$
$a=35.26$
$2a=70.5^\circ$ for the angle between $y=\sin 2x$ and $y=\cos 2x$
I am not quite sure about the solution for extending my solution to calculate angle between the curves $y=\sin 5x$ and $y=\cos 5x$. 
For $y=\sin 5x \rightarrow$ angle is $20.96^\circ$ 
For $y=\cos 5x \rightarrow$ angle is $42.74^\circ$ 

let $ f(x)=sin(2x)$ and $g(x)=cos(2x)$
So $ f'(x)=2 \cos(2x)$ and $g'(x)= -2 \sin(2x)$
$ f'(\frac{\pi}{8})=\sqrt 2 $ and $g'(\frac{\pi}{8})= -\sqrt 2$
so the angle between the two curves is $ \theta = 2 \tan^{-1}(\sqrt 2)$
for the second problem the intersection point is $x = \frac{\pi}{20}$
the angle between the two curves is $ \theta = 2 \tan^{-1}(\frac{5}{\sqrt 2})$
