Prove trig derivative (1 Viewer)

enigma_1 · Mar 11, 2014

How do you prove the derivative of y=sin x is equal to sin(pi/2 +x) ?

I know that's an identity but it says to prove right? Is there an actual method?

Shadowdude · Mar 11, 2014

enigma_1 said:
How do you prove the derivative of y=sin x is equal to sin(pi/2 +x) ?

I know that's an identity but it says to prove right? Is there an actual method?

Yes, but it's 3u.

$y=\sin(x) \implies \frac{dy}{dx}=\cos(x)$

$\sin\left ( \frac{\pi}{2}+x \right ) = \sin\left(\frac{\pi}{2}\right)\cos(x) + \cos\left(\frac{\pi}{2}\right)\sin(x) = \cos(x)$

braintic · Mar 13, 2014

Shadowdude said:
Yes, but it's 3u.

$y=\sin(x) \implies \frac{dy}{dx}=\cos(x)$

$\sin\left ( \frac{\pi}{2}+x \right ) = \sin\left(\frac{\pi}{2}\right)\cos(x) + \cos\left(\frac{\pi}{2}\right)\sin(x) = \cos(x)$

You don't need Extension trig for this.

I'll use degrees cause I can't be bothered using latex.

sin (90+x) = sin [90 - (-x)] = cos (-x) = cos x

Prove trig derivative (1 Viewer)

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Prove trig derivative (1 Viewer)

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