Math-trig question

Question

Given: tan A = 3/4, and cos B = -24/25, for A and B in quadrant III. Find values of following: cos 1/2 B

a. -√ 5/2

b. -√ 2/10

c. 1/50

d. -1/2

Answer 1

Since B lies in quadrant 3, π < B < 3π/2. So, π/2 < B/2 < 3π/4. Therefore, cos(B/2) is negative since B/2 lies in the second quadrant.

cos(B/2) = -√[(1+cosB)/2] = -√(1/50) = -1/(5√2) = -√2/10

Answer 2

cos B = -24/25

" " =-.96

B=163.789.....

3rd qu=253.789....

cos B/2=cos253.789/2

=cos126.894=.333.....