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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 $42.74^\circ$

hexaflexagonal
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lolisme
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    Which curve are you talking about when you write $y'(\frac{\pi}{8})=.707$? Also, when you define the angle $a$, you should make clear what it refers to. – hexaflexagonal Jun 25 '15 at 15:35

1 Answers1

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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})$

WW1
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