Question

If sin (A) = -12/13 with A in QIII, find cos (A/2).

Answer 1

5/13 in quadrants I and IIII and negative in the other two quadrants.

Answer 2

Use cos(B/2) = ± sqrt([1 + cos B] / 2) after finding cos

Answer 3

cos (A) = -5/13

Answer 4

cos (A) = 2 cos^2(A/2) - 1
-5/13 = 2 cos^2(A/2) - 1

solve for cos( A/2)

Answer 5

2 cos^2(A/2 = 8/13
cos^2(A/2) = 4/13
cos (A/2) = +- 2 / sqrt 13
the value must be negative (cos is neg in Q3)
so
cos(A/2) = -2/sqrt13