Theory and ExamplesRadians versus degrees: degree mode

Chapter 3, Problem 70E

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Problem 70E

Theory and Examples

Radians versus degrees: degree mode derivatives What happens to the derivatives of sin x and cos x if x is measured in degrees instead of radians? To find out, take the following steps.

a. With your graphing calculator or computer grapher in degree mode, graph Compare your estimate with π/180. Is there any reason to believe the limit should be π/180?

b. With your grapher still in degree mode, estimate

c. Now go back to the derivation of the formula for the derivative of sin x in the text and carry out the steps of the derivation using degree-mode limits. What formula do you obtain for the derivative?

d. Work through the derivation of the formula for the derivative of cos x using degree-mode limits. What formula do you obtain for the derivative?

e. The disadvantages of the degree-mode formulas become apparent as you start taking derivatives of higher order. Try it. What are the second and third degree-mode derivatives of sin x and cos x?