Find the exact value of cos(t/2) if sin(t)=-7/25

Question

Find the exact value of cos(t/2) if sin(t)=-7/25 and pi < t <3pi/2

Answer 1

You know what sine of t is (given), so you can compute the exact value of cosine of t, using Pythagorean identity).

The angle is said to be in the third quadrant, so the cosine of t is positive.

 

Now use the half angle formula; cos(t/2) = √[½•(1+cos t)]. Since t/2 will be in the second quadrant, this computed value is positive.