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Fungsi trigonometri
Kalkulator menghitung nilai fungsi trigonometri.
Rumus-rumus dan grafik disajikan pada masing-masing halaman.
Kalkulator
sinus
$$ \begin{aligned} & \sin\alpha \end{aligned} $$
kosinus
$$ \begin{aligned} & \cos\alpha \end{aligned} $$
tangen
$$ \begin{aligned} & \tan\alpha \end{aligned} $$
kotangen
$$ \begin{aligned} & \cot\alpha \end{aligned} $$
Rumus-rumus
segitiga siku-siku
A
B
C
a
b
c
α
β
$$ \begin{aligned} & \sin\alpha = \frac{a}{c} \ \ \ && \sin\beta = \frac{b}{c} \\ \\ & \cos\alpha = \frac{b}{c} && \cos\beta = \frac{a}{c} \\ \\ & \tan\alpha = \frac{a}{b} && \tan\beta = \frac{b}{a} \\ \\ & \cot\alpha = \frac{b}{a} && \cot\beta = \frac{a}{b} \end{aligned} $$
$$ \begin{aligned} &\sin^2\alpha + \cos^2\alpha = 1 \\ \\ &\tan\alpha \cdot \cot\alpha = 1 \ \Rightarrow \\ \\ &\cot\alpha = \frac{1}{\tan\alpha} \\ \\ &\tan\alpha = \frac{\sin\alpha}{\cos\alpha} \\ \\ &\cot\alpha = \frac{\cos\alpha}{\sin\alpha} \end{aligned} $$
$$ \begin{aligned} &\sin(\alpha + \beta) = \\& = \sin\alpha\cos\beta + \cos\alpha\sin\beta \\ \\ &\sin(\alpha - \beta) = \\& = \sin\alpha\cos\beta - \cos\alpha\sin\beta \\ \\ &\cos(\alpha + \beta) = \\& = \cos\alpha\cos\beta - \sin\alpha\sin\beta \\ \\ &\cos(\alpha - \beta) = \\& = \cos\alpha\cos\beta + \sin\alpha\sin\beta \\ \\ &\tan(\alpha + \beta) = \frac{\tan\alpha + \tan\beta}{1 - \tan\alpha\tan\beta} \\ \\ &\tan(\alpha - \beta) = \frac{\tan\alpha - \tan\beta}{1 + \tan\alpha\tan\beta} \end{aligned} $$
$$ \begin{aligned} &\sin\alpha + \sin\beta = \\& = 2\cdot\sin\frac{\alpha + \beta}{2}\cdot\cos\frac{\alpha - \beta}{2} \\ \\ &\sin\alpha - \sin\beta = \\& = 2\cdot\cos\frac{\alpha + \beta}{2}\cdot\sin\frac{\alpha - \beta}{2} \\ \\ &\cos\alpha + \cos\beta = \\& = 2\cdot\cos\frac{\alpha + \beta}{2}\cdot\cos\frac{\alpha - \beta}{2} \\ \\ &\cos\alpha - \cos\beta = \\& = -2\cdot\sin\frac{\alpha + \beta}{2}\cdot\sin\frac{\alpha - \beta}{2} \end{aligned} $$
$$ \begin{aligned} & \sin 2\alpha = 2\cdot\sin\alpha\cos\alpha \\ \\ & \cos 2\alpha = \cos^2\alpha - \sin^2\alpha \\ \\ & \tan 2\alpha = \frac{2\cdot\tan\alpha}{1 - {\tan}^2\alpha} \end{aligned} $$
$$ \begin{aligned} & \left|\sin\frac{\alpha}{2}\right| = \sqrt{\frac{1-\cos\alpha}{2}} \\ \\ & \left|\cos\frac{\alpha}{2}\right| = \sqrt{\frac{1+\cos\alpha}{2}} \\ \\ & \left|\tan\frac{\alpha}{2}\right| = \sqrt{\frac{1-\cos\alpha}{1+\cos\alpha}} \end{aligned} $$
$$ \begin{aligned} & \sin(-\alpha) = -\sin\alpha \\ \\ & \cos(-\alpha) = \cos\alpha \\ \\ & \tan(-\alpha) = -\tan\alpha \\ \\ & \cot(-\alpha) = -\cot\alpha \end{aligned} $$
Skor
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fungsi trigonometri
✕
sinus
kosinus
tangen
kotangen
luas dan keliling
☰
lingkaran
segitiga
segitiga siku-siku
persegi
persegi panjang
belah ketupat
jajar genjang
trapesium
segi lima
segi enam
segi banyak
teorema Pythagoras
volume dan luas permukaan
☰
kubus
balok
tabung
kerucut
bola
prisma
limas
persentase
perkalian silang
persamaan
☰
persamaan linear
persamaan kuadrat
sistem persamaan linear
rata-rata
☰
rata-rata aritmetika
rata-rata terbobot
pangkat dan akar
☰
pangkat dua
pangkat tiga
pangkat ke-n
akar kuadrat
akar pangkat tiga
akar ke-n
logaritma
☰
logaritma
logaritma alami
logaritma umum
konversi satuan
☰
panjang
luas
volume
massa
kecepatan
suhu
sudut
tekanan
daya
energi
waktu
energi dan bahan bakar
☰
konsumsi listrik
konsumsi bahan bakar
konsumsi gas