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. Radians versus degrees: degree mode derivatives What hap- pens 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 sin h f(h) = and estimate lim,-of(h). Compare your estimate with T/180. Is there any reason to believe the limit should be T/180? b. With your grapher still in degree mode, estimate cos h - 1 lim c. Now go back to the derivation of the formula for the deriva- tive of sin x in the text and carry out the steps of the deriva- tion using degree-mode limits. What formula do you obtain for the derivative? d. Work through the derivation of the formula for the deriva- tive of cos x using degree-mode limits. What formula do you obtain for the derivative? e. The disadvantages of the degree-mode formulas become ap- parent 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?

. Radians versus degrees: degree mode derivatives What hap- pens 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 sin h f(h) = and estimate lim,-of(h). Compare your estimate with T/180. Is there any reason to believe the limit should be T/180? b. With your grapher still in degree mode, estimate cos h - 1 lim c. Now go back to the derivation of the formula for the deriva- tive of sin x in the text and carry out the steps of the deriva- tion using degree-mode limits. What formula do you obtain for the derivative? d. Work through the derivation of the formula for the deriva- tive of cos x using degree-mode limits. What formula do you obtain for the derivative? e. The disadvantages of the degree-mode formulas become ap- parent 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?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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. Radians versus degrees: degree mode derivatives What hap- pens 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 sin h f(h) = and estimate lim,-of(h). Compare your estimate with T/180. Is there any reason to believe the limit should be T/180? b. With your grapher still in degree mode, estimate cos h - 1 lim c. Now go back to the derivation of the formula for the deriva- tive of sin x in the text and carry out the steps of the deriva- tion using degree-mode limits. What formula do you obtain for the derivative? d. Work through the derivation of the formula for the deriva- tive of cos x using degree-mode limits. What formula do you obtain for the derivative? e. The disadvantages of the degree-mode formulas become ap- parent 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?
Transcribed Image Text:. Radians versus degrees: degree mode derivatives What hap- pens 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 sin h f(h) = and estimate lim,-of(h). Compare your estimate with T/180. Is there any reason to believe the limit should be T/180? b. With your grapher still in degree mode, estimate cos h - 1 lim c. Now go back to the derivation of the formula for the deriva- tive of sin x in the text and carry out the steps of the deriva- tion using degree-mode limits. What formula do you obtain for the derivative? d. Work through the derivation of the formula for the deriva- tive of cos x using degree-mode limits. What formula do you obtain for the derivative? e. The disadvantages of the degree-mode formulas become ap- parent 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?
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