Tangent Angle Calculator

Tangent of an Angle

In a right triangle, the tangent of angle $\theta$ is the ratio of the opposite side to the adjacent side:

$$\tan(\theta) = \frac{a}{b}$$

Tangent can also be expressed using sine and cosine: $\tan(\theta) = \sin(\theta) / \cos(\theta)$.

If the opposite side is 21 and the adjacent side is 8:

$$\tan(\theta) = \frac{21}{8} = 2.625$$

Is tangent x/y or y/x?

On the unit circle, coordinates are $(\cos\theta, \sin\theta)$, so tangent is $y/x = \sin\theta/\cos\theta$, not $x/y$.

When is tangent undefined?

Tangent is undefined when $\cos\theta = 0$, which occurs at odd multiples of $90°$ ($\pi/2$ radians).

What is tan(45°)?

$\tan(45°) = 1$, because in a 45-45-90 triangle the opposite and adjacent sides are equal.

How do I find the angle from tangent?

Use the inverse tangent: $\theta = \arctan(a/b)$ when you know the opposite and adjacent sides.