Вычисли и напиши решение

Привет! Давай решим эти примеры вместе.

1) cos(-π/6) * sin(-π/3) + tg(-π/4)

• cos(-π/6) = cos(π/6) = √3/2
• sin(-π/3) = -sin(π/3) = -√3/2
• tg(-π/4) = -tg(π/4) = -1

Подставляем значения:

(√3/2) * (-√3/2) - 1 = -3/4 - 1 = -7/4 = -1.75

Ответ: -1.75

2) (1 + tg²(-π/6)) / (1 + ctg²(-π/6))

• tg(-π/6) = -tg(π/6) = -1/√3
• tg²(-π/6) = 1/3
• ctg(-π/6) = -ctg(π/6) = -√3
• ctg²(-π/6) = 3

Подставляем значения:

(1 + 1/3) / (1 + 3) = (4/3) / 4 = 1/3

Ответ: 1/3

3) 2 * sin(-π/6) * cos(-π/6) + tg(-π/3) + sin²(-π/4)

• sin(-π/6) = -sin(π/6) = -1/2
• cos(-π/6) = cos(π/6) = √3/2
• tg(-π/3) = -tg(π/3) = -√3
• sin(-π/4) = -sin(π/4) = -√2/2
• sin²(-π/4) = (-√2/2)² = 1/2

Подставляем значения:

2 * (-1/2) * (√3/2) - √3 + 1/2 = -√3/2 - √3 + 1/2 = -3√3/2 + 1/2 = (1 - 3√3) / 2

Ответ: (1 - 3√3) / 2

4) cos(-π) + ctg(-π/2) - sin(-3π/2) + ctg(-π/4)

• cos(-π) = cos(π) = -1
• ctg(-π/2) = -ctg(π/2) = 0
• sin(-3π/2) = -sin(3π/2) = -(-1) = 1
• ctg(-π/4) = -ctg(π/4) = -1

Подставляем значения:

-1 + 0 - 1 - 1 = -3

Ответ: -3

5) (3 - sin²(-π/3) - cos²(-π/3)) / (2 * cos(-π/4))

• sin(-π/3) = -sin(π/3) = -√3/2
• sin²(-π/3) = 3/4
• cos(-π/3) = cos(π/3) = 1/2
• cos²(-π/3) = 1/4
• cos(-π/4) = cos(π/4) = √2/2

Подставляем значения:

(3 - 3/4 - 1/4) / (2 * √2/2) = (3 - 1) / √2 = 2 / √2 = √2

Ответ: √2

6) 2 * sin(-π/6) + 3 + 7.5 * tg(-π) + 1/8 * cos(3π/2)

• sin(-π/6) = -sin(π/6) = -1/2
• tg(-π) = -tg(π) = 0
• cos(3π/2) = 0

Подставляем значения:

2 * (-1/2) + 3 + 7.5 * 0 + 1/8 * 0 = -1 + 3 + 0 + 0 = 2

Ответ: 2

Надеюсь, теперь тебе всё понятно! Если есть ещё вопросы, обязательно задавай.