Cotangent

Definition

Cotangent is a trigonometric function defined as the reciprocal of the tangent function. It can be expressed as $\cot(\theta) = \frac{1}{\tan(\theta)}$ or $\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$.

5 Must Know Facts For Your Next Test

1. Cotangent is undefined when sine is zero because division by zero is undefined.
2. The cotangent function has vertical asymptotes where the sine function is zero, i.e., at $n\pi$ for integer values of $n$.
3. The period of the cotangent function is $\pi$, meaning it repeats every $\pi$ units.
4. Cotangent values are positive in the first and third quadrants and negative in the second and fourth quadrants.
5. The graph of the cotangent function decreases from left to right within each period.

Review Questions

• What is the relationship between cotangent and tangent?
• At which points on the unit circle is cotangent undefined?
• How does the period of the cotangent function compare to that of other trigonometric functions like sine and cosine?

Related terms

Tangent: A trigonometric function defined as $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$. It represents the ratio of the opposite side to the adjacent side in a right-angled triangle.

Secant: $Secant (sec)$ is a trigonometric function that is the reciprocal of cosine, defined as $sec(\theta) = \frac{1}{cos(θ)}$.

Cosecant: $Cosecant (csc)$ is a trigonometric function that is the reciprocal of sine, defined as $csc (𝜃)= \frac {1} {sin (𝜃)}$.