# California University Long Beach Trigonometric Functions Series Question

Question Description

I’m working on a calculus multi-part question and need support to help me learn.

9. The following questions have to do with how to approximate cos 50° using series.
a. (2 points) Suppose you wish to find a good approximation for cos 50º. Which series do you think will converge
faster (that is, need less terms to be summed) to this value, the MacLaurin series centered at zero or a Taylor series
centered at a ? Give a single sentence explanation of your answer.
b. (3 points) Approximate cos 50° by plugging an appropriate value for x into the MacLaurin series for the cosine
function and adding first four terms.
C. (4 points) Find the first four terms of the Taylor series for the cosine function centered at a =
TT
4
77 중
d. (2 points) Approximate cos 50° by plugging an appropriate value for x into your Taylor series in part (c) and adding
first four terms.
e. (2 points) Using your calculator, compute cos 50°; which of your approximations was closer, part (b) and part (d)?