Question

If y = sinx^o and $\frac{dy}{dx}$ = k cos x^o , then k = ________________.

Answer 1

$y=\sin x°$

$\Rightarrow y=\sin \left(\frac{\mathrm{\pi }}{180}x\right)\left(180°=\mathrm{\pi }\mathrm{radians}\right)$

Differentiating both sides with respect to x, we get

$\frac{dy}{dx}=\frac{d}{dx}\sin \left(\frac{\mathrm{\pi }}{180}x\right)$

$\Rightarrow \frac{dy}{dx}=\cos \left(\frac{\mathrm{\pi }}{180}x\right)\times \frac{d}{dx}\left(\frac{\mathrm{\pi }}{180}x\right)$

$\Rightarrow \frac{dy}{dx}=\cos x°\times \frac{\mathrm{\pi }}{180}$

$\Rightarrow \frac{dy}{dx}=\frac{\mathrm{\pi }}{180}\cos x°$

Comparing with $\frac{dy}{dx}=k\cos x°$, we get

$k=\frac{\mathrm{\pi }}{180}$


If y = sinx^o and $\frac{dy}{dx}$ = k cosx^o , then k = $\underline{\frac{\mathrm{\pi }}{180}}$.