If cos (t) = - 9/11 where pi

cos (2t) =

sin (2t) =

cos (t/2) =

sin (t/2) =

Sin (t) = √ (1 - (-9/11) ²) = √ (1 - 81/121) = √ 40/121

sin (t) = - 2 √10 / 11

cos (2 t) = cos² t - sin² t = 81/121 - 40 / 121 = 41 / 121

sin (2 t) = 2 sin t cos t = 2 · ( - 2 √10/11) · ( - 9 / 11) = 36√10 / 121

cos (t/2) = √ (1 + cos t) / 2 = 1 / √11

sin (t/2) = √ (1 - cos t) / 2 = √ (10/11)