Question

Suppose pi < theta < 3pi/2 and that tan(theta) = 7/3, find cos(theta/2) How would I go about doing this problem, and how would i know what quadrant it is in

Answer 1

its in quadrant III

Answer 2

So, lets draw a trianglecos(theta) = adj/hyp

Answer 3

after you find that, use half-angle and find cos(theta/2)

Answer 4

How would I go about finding which quadrant the half angle is in, if i remember correctly with a half angle in quadrant 3 it is either in quadrant 3 or 1

Answer 5

cos(theta)= -3rt(58)/58
cos(theta/2) = rt((cos(theta)+1)/2)

Answer 6

take sin(2theta) if it is negative, then the sign for cos(theta/2) will be negative