What happens to the derivative 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 grapher in degree mode, graph
f(h)=Sin h/h
and estimate lim h ▬>0 f(h). Compare your estimate with pi/180. Is there any reason to believe the limit should be pi/180?
b) With your grapher in degree mode, estimate
lim h ▬>0 cos h-1/h
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) Derive the formula for the derivative of cos x using degree mode limits.
e) The disadvantages of the degree mode formulas become apparent as you start taking derivatives of higher order. What are the second and third degree mode derivatives of sin x and cos x?