Задание 11.1

Найдите значения выражения:

1)sin ⁡ 390∘;4)tg (−210∘);

2)tg 780∘;5)cos ⁡ 300∘;

3)sin ⁡ (−390∘);6)sin ⁡ 5π 3 .

Answers

[10px,border : 3pxsolidblue]sin ⁡ (x − 2πn) = sin ⁡ x = sin ⁡ (x + 2πn).

[10px,border : 3pxsolidblue]cos ⁡ (x − 2πn) = cos ⁡ x = cos ⁡ (x + 2πn).

[10px,border : 3pxsolidblue]tg (x − 2πn) = tg x = tg (x + 2πn).

1.
sin ⁡ 390∘ = sin ⁡ (360∘ + 30∘) = sin ⁡ (2π + 30∘) = sin ⁡ 30∘ = 1 2

2.
tg 780∘ = tg (720∘ + 60∘) = tg (4π + 60∘) = tg 60∘ = 3

3.
sin ⁡ (−390∘) = −sin ⁡ (390∘) = −sin ⁡ (2π + 30∘) = −sin ⁡ 30∘ = −1 2

4.
tg (−210∘) = −tg 210∘ = −tg (π + 30∘) = −tg 30∘ = −3 3 .

5.
cos ⁡ 300∘ = cos ⁡ (−(60∘− 2π)) = cos ⁡ (60∘− 2π) = cos ⁡ 60∘ = 1 2

6.
sin ⁡ 5π 3 = sin ⁡ (2π −π 3 ) = −sin ⁡ (π 3 − 2π) = −sin ⁡ π 3 = −3 2 .

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2021-11-09 09:20
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