Question

Sin10π/3= Cos10π/3= tg10π/3= ctg10π/3=

Answer 1

Ответ:

Объяснение:

sin10π/3=sin600° =sin(360°+240°)=sin240°=sin(180°+60°)=-sin60°=-√3/2

Cos10π/3=Cos600°=Cos(360°+240°)=Cos240°=Cos(180°+60°)=-Cos60°=-1/2

tg10π/3=tg600°=tg(360°+240°)=tg240°=tg(180°+60°)=tg60°=√3

ctg10π/3=ctg600°=ctg(360°+240°)=ctg240°=ctg(180°+60°)=ctg60°=1/√3

Answer 2

Для решения данного вопроса используем формулы для тригонометрических функций.

1. Синус:

sin(10π/3) = sin(π - 10π/3) = sin(π/3) = √3/2

2. Косинус:

cos(10π/3) = cos(π - 10π/3) = cos(π/3) = 1/2

3. Тангенс:

tg(10π/3) = sin(10π/3) / cos(10π/3) = (√3/2) / (1/2) = √3

4. Котангенс:

ctg(10π/3) = 1 / tg(10π/3) = 1 / √3 = √3/3

Итак, получаем:

sin(10π/3) = √3/2 cos(10π/3) = 1/2 tg(10π/3) = √3 ctg(10π/3) = √3/3