Trignometry finding values

Question

Find sin (A/2) and cos(A/2)

If1. Cot A = -4/3. A in Quadrant 4

2. sin A= -12/13 .A in Quadrant 3

3.cos A= -5/3. A in Quadrant 2

Answer 1

Here is an answer to the first problem. The others are done in a similar manner.

Since ∠A lies in quadrant 4, 270° < A < 360°.

So, 135° < A/2 < 180° (A/2 lies in quadrant 2.

Therefore, sin(A/2) > 0 and cos(A/2) < 0

Using the half angle formulas for sine and cosine, we have:

sin(A/2) = √[(1-cosA)/2] = √[(1 - 4/5)/2 = √(1/10) = √10/10

cos(A/2) = -√[(1+cosA)/2] = -√[(1+4/5)/2 = -√(9/10) = -3√10/10

Answer 2

cot=cos/sin

-4/3=(cosa/2)/(sina/2)

a=-73.9 or -286.1

cos-286.1=.277

sin-286.1=.961

sina=-12/13

a=-67.38 or -247.38

cos-247.38=-.385

sin-247.38=.923

cosa=-5/3

a=?