Question

Найти значение
Sin a , tg a , cos a , если ctg a = 8/15 , п<a<3п/2

Answer 1

tga = 1/ctga = 15/8

tga = sina/cosa = 15/8 = 1,875
sina = 1,875cosa

cosa = -√(1-sin²a)

sina = -15/8√(1-sin²a)
sin²a = 225/64(1-sin²a)
289/64sin²a = 225/64
sin²a = 225/289
sina = -15/17
cosa = -√(1-225/289)=-8/17

Ответ: -15/17; 15/8; -8;17