Дано: Cos a =2/5 3П/2 Найти: Sin a, sin 2 a, cos 2 a, tg a, cos (П/3+ a), sin (a-П/6)

Question

Дано:
Cos a =2/5 3П/2 Найти:
Sin a, sin 2 a, cos 2 a, tg a, cos (П/3+ a), sin (a-П/6)

Answer 1

Cosa=2/5
sina=√(1-cos²a)=√(1-4/25)=√(21/25)=√21/5
sin2a=2sinacosa=2*2/5*√21/5=4√21/25
cos2a=cos²a-sin²a=4/25-21/25=-17/25
tga=sina/cosa=√21/5:2/5=√21/5*5/2=√21/2
cos(π/3+a)=cosπ/3cosa-sinπ/3sina=1/2*2/5-√3/2*√21/5=1/5-3√7/10=(2-3√7)/10
sin(a-π/6)=sinacosπ/6-cosasinπ/6=√21/5*√3/2-2/5*1/2=3√7/10-1/5=(3√7-2)/10