Given: Cot A= -8/15, where cos A > 0 and cos B = 5/13 where 0< B< pi/2

Answer 1

cosine is positive in QI and QIV

cotangent is negative in QII and QIV

A is in QIV

Use Pythagoras to determine sin A and cos A

B is in Qi

Use Pythagoras to determine sin B

Substitute values into appropriate formula.

Answer 2

cos2A = cos^2A - sin^2A = (15/17)^2 - (-8/17)^2 = (225-64)/17^2 = 161/289

or cos2A = 2cos^2A -1 = 2(15/17)^2 =450/289-1 = 450/289-289/289 = 161/289

= about 0.557

sinB/2 = sqr((1-cosB)/2) = sqr(1/2 - 5/26) =sqr(8/26) = sqr(4/13) =2sqr(1/13) = about 0.555

cos2A is slightly larger than sinB/2