Cotangent function

Definition

The cotangent function, denoted as $\cot(x)$, is the reciprocal of the tangent function. It can be defined as $\cot(x) = \frac{1}{\tan(x)}$ or $\cot(x) = \frac{\cos(x)}{\sin(x)}$.

5 Must Know Facts For Your Next Test

1. $\cot(x)$ has vertical asymptotes where $x = k\pi$, where $k$ is an integer.
2. The period of the cotangent function is $\pi$, meaning that $\cot(x + \pi) = \cot(x)$.
3. $\cot(x)$ is undefined at multiples of $\pi$, i.e., at points where the sine function is zero.
4. The cotangent function decreases from positive infinity to negative infinity within each period.
5. $\int \cot(x) \, dx = \ln|\sin(x)| + C$ is a common integral involving the cotangent function.

Review Questions

• What are the vertical asymptotes of the cotangent function?
• How would you express $\cot(x)$ in terms of sine and cosine?
• What is the period of the cotangent function?

Related terms

Tangent Function: $\tan(x)$ represents the ratio of sine to cosine, defined as $\tan(x) = \frac{\sin(x)}{\cos(x)}$.

Sine Function: $\sin(x)$ represents a fundamental trigonometric function describing y-coordinates on the unit circle.

Cosine Function: $\cos(x)$ represents a fundamental trigonometric function describing x-coordinates on the unit circle.