Círculo Unitario
Arrastra para rotar
Ángulo
0.0°
0 rad
Seno
0.000
Coseno
1.000
Tangente
0.000
Cosecante
∞
Secante
1.000
Cotangente
∞
Básicas
$\tan \theta = \frac{\sin \theta}{\cos \theta}$
tan θ = sin θ / cos θ
0.000
$\cot \theta = \frac{\cos \theta}{\sin \theta}$
cot θ = cos θ / sin θ
∞
$\sec \theta = \frac{1}{\cos \theta}$
sec θ = 1 / cos θ
1.000
$\csc \theta = \frac{1}{\sin \theta}$
csc θ = 1 / sin θ
∞
Pitagóricas
$\sin^2\theta + \cos^2\theta = 1$
sin²θ + cos²θ = 1
1.000
$\tan^2\theta + 1 = \sec^2\theta$
tan²θ + 1 = sec²θ
1.000
$1 + \cot^2\theta = \csc^2\theta$
1 + cot²θ = csc²θ
∞
Par/Impar
$\sin(-\theta) = -\sin \theta$
sin(-θ) = -sin θ
0.000
$\cos(-\theta) = \cos \theta$
cos(-θ) = cos θ
1.000
$\tan(-\theta) = -\tan \theta$
tan(-θ) = -tan θ
0.000
Reducción de Potencia
$\sin^2\theta = \frac{1-\cos(2\theta)}{2}$
sin²θ = (1-cos(2θ))/2
0.000
$\cos^2\theta = \frac{1+\cos(2\theta)}{2}$
cos²θ = (1+cos(2θ))/2
1.000
Complementarios
$\sin(90^\circ-\theta) = \cos \theta$
sin(90°-θ) = cos θ
1.000
$\cos(90^\circ-\theta) = \sin \theta$
cos(90°-θ) = sin θ
0.000
$\tan(90^\circ-\theta) = \cot \theta$
tan(90°-θ) = cot θ
0.000
$\sec(90^\circ-\theta) = \csc \theta$
sec(90°-θ) = csc θ
0.000
Ángulos Dobles y Mitad
$\sin(2\theta) = 2 \sin \theta \cos \theta$
sin(2θ) = 2 sin θ cos θ
0.000
$\cos(2\theta) = \cos^2\theta - \sin^2\theta$
cos(2θ) = cos²θ - sin²θ
1.000
$\tan(2\theta) = \frac{2\tan\theta}{1-\tan^2\theta}$
tan(2θ) = 2tanθ / (1-tan²θ)
0.000
$\sin(\frac{\theta}{2}) = \pm\sqrt{\frac{1-\cos\theta}{2}}$
sin(θ/2) = √((1-cosθ)/2)
0.000
$\cos(\frac{\theta}{2}) = \pm\sqrt{\frac{1+\cos\theta}{2}}$
cos(θ/2) = √((1+cosθ)/2)
1.000
$\tan(\frac{\theta}{2}) = \frac{1-\cos\theta}{\sin\theta}$
tan(θ/2) = (1-cosθ)/sinθ
0.000
Valores Notables
| Grados | Radianes | sin θ | cos θ | tan θ | csc θ | sec θ | cot θ |
|---|---|---|---|---|---|---|---|
| $0^\circ$ | $0$ | $0$ | $1$ | $0$ | $\infty$ | $1$ | $\infty$ |
| $30^\circ$ | $\frac{\pi}{6}$ | $\frac{1}{2}$ | $\frac{\sqrt{3}}{2}$ | $\frac{\sqrt{3}}{3}$ | $2$ | $\frac{2\sqrt{3}}{3}$ | $\sqrt{3}$ |
| $45^\circ$ | $\frac{\pi}{4}$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $1$ | $\sqrt{2}$ | $\sqrt{2}$ | $1$ |
| $60^\circ$ | $\frac{\pi}{3}$ | $\frac{\sqrt{3}}{2}$ | $\frac{1}{2}$ | $\sqrt{3}$ | $\frac{2\sqrt{3}}{3}$ | $2$ | $\frac{\sqrt{3}}{3}$ |
| $90^\circ$ | $\frac{\pi}{2}$ | $1$ | $0$ | $\infty$ | $1$ | $\infty$ | $0$ |
| $120^\circ$ | $\frac{2\pi}{3}$ | $\frac{\sqrt{3}}{2}$ | $-\frac{1}{2}$ | $-\sqrt{3}$ | $\frac{2\sqrt{3}}{3}$ | $-2$ | $-\frac{\sqrt{3}}{3}$ |
| $135^\circ$ | $\frac{3\pi}{4}$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $-1$ | $\sqrt{2}$ | $-\sqrt{2}$ | $-1$ |
| $150^\circ$ | $\frac{5\pi}{6}$ | $\frac{1}{2}$ | $-\frac{\sqrt{3}}{2}$ | $-\frac{\sqrt{3}}{3}$ | $2$ | $-\frac{2\sqrt{3}}{3}$ | $-\sqrt{3}$ |
| $180^\circ$ | $\pi$ | $0$ | $-1$ | $0$ | $\infty$ | $-1$ | $\infty$ |
| $210^\circ$ | $\frac{7\pi}{6}$ | $-\frac{1}{2}$ | $-\frac{\sqrt{3}}{2}$ | $\frac{\sqrt{3}}{3}$ | $-2$ | $-\frac{2\sqrt{3}}{3}$ | $\sqrt{3}$ |
| $225^\circ$ | $\frac{5\pi}{4}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $1$ | $-\sqrt{2}$ | $-\sqrt{2}$ | $1$ |
| $240^\circ$ | $\frac{4\pi}{3}$ | $-\frac{\sqrt{3}}{2}$ | $-\frac{1}{2}$ | $\sqrt{3}$ | $-\frac{2\sqrt{3}}{3}$ | $-2$ | $\frac{\sqrt{3}}{3}$ |
| $270^\circ$ | $\frac{3\pi}{2}$ | $-1$ | $0$ | $\infty$ | $-1$ | $\infty$ | $0$ |
| $300^\circ$ | $\frac{5\pi}{3}$ | $-\frac{\sqrt{3}}{2}$ | $\frac{1}{2}$ | $-\sqrt{3}$ | $-\frac{2\sqrt{3}}{3}$ | $2$ | $-\frac{\sqrt{3}}{3}$ |
| $315^\circ$ | $\frac{7\pi}{4}$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $-1$ | $-\sqrt{2}$ | $\sqrt{2}$ | $-1$ |
| $330^\circ$ | $\frac{11\pi}{6}$ | $-\frac{1}{2}$ | $\frac{\sqrt{3}}{2}$ | $-\frac{\sqrt{3}}{3}$ | $-2$ | $\frac{2\sqrt{3}}{3}$ | $-\sqrt{3}$ |
| $360^\circ$ | $2\pi$ | $0$ | $1$ | $0$ | $\infty$ | $1$ | $\infty$ |