Real and Complex Numbers

1.

2.

sin(180° − x) = sin x
•sin(180° + x) = −sin x
•cos(180° − x) = −cos x
•cos(180° + x) = −cos x
•tg(180° ± x) = tg x

3.

sin(210°)
•210° = 180° + 30°
•sin(210°) = −sin(30°) = −1/2

4.

sin(α + β) = sinα·cosβ + cosα·sinβ
sin(α − β) = sinα·cosβ − cosα·sinβ
cos(α + β) = cosα·cosβ − sinα·sinβ
cos(α − β) = cosα·cosβ + sinα·sinβ
tg(α ± β) = (tgα ± tgβ) / (1 ∓ tgα·tgβ)

5.

sin(45° + 30°)
sin(75°) = sin45°·cos30° +
cos45°·sin30 = (√2/2)·(√3/2) +
(√2/2)·(1/2)
"Complex
Number."Britannica,https://www.britannica.com/science/complex-number.
Accessed 10 Oct 2021

6.

•sin(2α) = 2sinα·cosα
•cos(2α) = cos²α − sin²α
•cos(2α) = 1 − 2sin²α
•cos(2α) = 2cos²α − 1
•tg(2α) = 2tgα / (1 − tg²α)

7.

)
sin(60°) = 2sin30°·cos30° = 2·(1/2)·(√3/2) = √3/2