Find cos 2a and cos A/2

Question

If sin A= − 65/65 with 180° ≤ A ≤ 270°

Answer 1

sinA = sqr65/65 = 1/sqr65= opposite side/hypotenuse

adjacent side = sqr64 = 8

A = 187.125 degrees

cosA = adjacent side/hypotenuse = 8/sqr65 = 8sqr65/65

cos2A = cos^2(A) - sin^2(A) = 64/65 - 1/65 = 63/65

cos(187.125) = -.99228

cos(374.25) = cos14.25 = .9692

cos93.563 =-.0621

cos(A/2) = -sqr((1+cosA)/2) = -sqr((1+8sqr65)/2)