Kesamaan Trigonometri

Kesamaan ganjil-genap

$sin(-x) = -sin x$

$cos(-x) = cos x$

$tan(-x) = -tan x$

Kesamaan Pythagoras

$sin^2 x + cos^2 x = 1$

$1 + tan^2 x = sec^2 x$

$1 + cot^2 x = csc^2 x$

Kesamaan penambahan

$sin (x + y) = sin x cos y + cos x sin y$

$cos (x + y) = cos x cos y - sin x sin y$

$tan (x + y) = \frac{tan x + tan y}{1 - tan x tan y}$

Kesamaan sudut-ganda

$sin 2x = 2 sin x cos x$

$cos 2x = cos^2 x - sin^2 x = 2 cos^2 x - 1 = 1 - 2 sin^2 x$

Kesamaan setengah-sudut

$sin^2 x = \frac{1 - cos 2x}{2}$

$cos^2 x = \frac{1+cos 2x}{2}$

Kesamaan jumlah

$sin x + sin y = 2 sin (\frac{x + y}{2}) cos (\frac{x - y}{2})$

$cos x + cos y = 2 cos (\frac{x + y}{2}) cos (\frac{x - y}{2})$

Kesamaan hasil kali

$sin x sin y = -\frac{1}{2} [cos (x + y) - cos (x - y)]$

$cos x cos y = \frac{1}{2} [cos ( x + y) + cos (x - y)]$

$sin x cos y = \frac{1}{2} [sin (x + y) + sin (x - y)]$

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