Question

If $x$ is measured in degrees, then $\frac{d}{dx}(\cos x)$ is equal to

• A. $-\sin x$
• B. $-\left(\frac{180}{\mathrm{\pi }}\right)\sin x$
• C. $-\left(\frac{\mathrm{\pi }}{180}\right)\sin x$
• D. $\sin x$

Answer 1

The correct option is C

$-\left(\frac{\mathrm{\pi }}{180}\right)\sin x$

Explanation for the correct option:

Step 1: Convert degree into radian:

Let $y=\cos x°$

We know that $\mathbf{1}\mathbf{°}\mathbf{=}\frac{\mathbf{\pi }}{\mathbf{180}}\mathbf{}\mathit{r}\mathit{a}\mathit{d}\mathit{i}\mathit{a}\mathit{n}$

So, $y=\cos \left(\frac{\mathrm{\pi x}}{180}\right)$

Step 2: Differentiating with respect to $\mathit{x}$ both sides:

$$\begin{gathered} \frac{dy}{dx}=-\sin \left(\frac{\mathrm{\pi x}}{180}\right)\times \frac{\pi }{180}\left[\because \frac{d\left(\mathrm{cosx}\right)}{\mathrm{dx}}=\mathrm{sinx}\right] \\ =-\frac{\pi }{180}\sin \left(\frac{\mathrm{\pi x}}{180}\right) \\ =-\frac{\pi }{180}\sin x° \end{gathered}$$

Hence, Option (C) is the correct answer.