Kesamaan Trigonometri

02 Apr 2009 4 Comments

by eena in matematika Tags: ,

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)]

4 Comments (+add yours?)

  1. adit38
    Apr 02, 2009 @ 15:15:55

    Wah bagus….., tambahin cerita jg dong…

    Reply

  2. Ahmad Priatama
    Mar 29, 2011 @ 22:50:46

    makasih, berguna banget ni buat ngerjain kalkulus

    Reply

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