Chapter 4.1, Problem 70E

To determine

To find: the given statement is true or false and to justify the answer.

Answer to Problem 70E

The given statement is false because the derivative rule $\frac{d}{dx}\left(\sin x\right)=\cos x$ is only valid when $x$ is measured in radians.

Explanation of Solution

Given information:

  $\frac{d}{dx}\left(\sin x\right)=\cos x$

Calculation:

The derivative rule $\frac{d}{dx}\left(\sin x\right)=\cos x$ is valid when we measure the input $x$ is measured in radians. It is not valid when we measure it in degrees.

The derivative $\frac{d}{dx}\left(\sin x\right)\text{is}\frac{\pi }{180}\cos x$ if the input $x$ is measure in degrees.

Thus we can conclude that the given statement is false.