Question

The differentiation formula $\frac{d}{dx}\left(\sin x\right)=\cos x$is valid only if x is measured in radians. In this exercise, you will explore why this derivative relationship does not hold if x is measured in degrees.

(a) Set your calculator to degree mode, and sketch a graph of $\sin x$that shows at least two periods. If the derivative of $\sin x\mathrm{is}\cos x,$then the slope of your graph at $x=0$should be equal to $\cos 0=1.$Use your graph to explain why this is not the case when we use degrees.

(Hint: Think about your graphing window scale.)

(b) Now set your calculator back to radians mode!

Short answer

(a) In degree, the slope of the graph of $\sin x\mathrm{at}x=0$is very small so it is not equal to $\cos 0=1.$

(b) The graph of $\sin x\&\cos x$in radian is following.

Step-by-step solution

Step 1. Given information.   

The given differential formula is$\frac{d}{dx}\sin x=\cos x$

Step 1. Part (a) 

Plot the graph of $\sin x\&\cos x$in radian.

Plot the graph of $\sin x\&\cos x$in degrees.

In degree, the slope of the graph of $\sin x$at $x=0$is very small and not equal to$\cos 0=1.$

Step 3. Part (b)

Plot the graph of $\sin x\&\cos x$in radian.