Tangent

Definition

A tangent is a trigonometric function represented as $\tan(\theta)$, which is the ratio of the sine and cosine of an angle: $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$. It is undefined when $\cos(\theta) = 0$.

5 Must Know Facts For Your Next Test

1. $\tan(0) = 0$ because $\sin(0) = 0$ and $\cos(0) = 1$.
2. The tangent function has vertical asymptotes where $\cos(\theta) = 0$, such as at $90^\circ$ or $270^\circ$.
3. The period of the tangent function is $180^\circ$ or $π$ radians.
4. Tangent functions are odd functions, meaning that $ \tan(-x) = - \tan(x)$.
5. The graph of the tangent function repeats every period with no maximum or minimum values, extending to infinity.

Review Questions

• What is the value of $ \tan (45^ \circ)$?
• Why does the tangent function have vertical asymptotes?
• What is the period of the tangent function?

Related terms

Sine Function: The sine of an angle in a right triangle is the ratio of the length of the opposite side to the hypotenuse: $\sin(\theta) = \frac{opposite}{hypotenuse}$.

Cosine Function: The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the hypotenuse: $\cos(\theta) = \frac{adjacent}{hypotenuse}$.

Cotangent: The cotangent is a trigonometric function defined as $\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$, which is also $\frac{1}{\tan(\theta)}$.