Question

If cos(t)=−9/11 where pi
cos(2t) =
sin(2t)=
cos(t/2)=
sin(t/2)=

Answer 1

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 )