given that P (θ) = (1/2, -√ 3/2) determine the following

Question

a. which quadrant does θ terminate?

b. determine the value of the central angle θ for 0 ≤ θ < 2π.

c. determine the values of the central angle θ for -2π ≤ θ < 4π. how is that related to coterminal angles

Answer 1

a) It is in Quadrant IV because x is positive and y is negative.

b) The central angle is 5pi/3, We know this from the Unit Circle.

c) In general any coterminal angle would be stated as 5pi/3 + 2pin (or n2pi) where n is any integer. For this problem we only want values between -2pi and 4pi so we will list all coterminal angles as follows.

{-pi/3,5pi/3,11pi/3}