Question

If $x$ is measured in degree, then $\frac{d}{dx}\left(\cos x\right)$ is equal to:

• A. $-\sin x$
• B. $-\frac{180}{\pi }\sin x$
• C. $-\frac{\pi }{180}\sin x$
• D. $\sin x$

Answer 1

Answer: (C)

$-\frac{\pi }{180}\sin x$

$x$ degree $=\frac{\pi }{180}x$ radian

Hence $\frac{d}{dx}\left(\cos x\right)=\frac{d}{dx}\left(\cos \frac{\pi .x}{180}\right)=-\sin x\frac{d}{dx}\left(\frac{\pi }{180}x\right)=-\frac{\pi }{180}\sin x$