Secant function

Definition

The secant function, denoted as $\sec(\theta)$, is the reciprocal of the cosine function. It is defined as $\sec(\theta) = \frac{1}{\cos(\theta)}$.

5 Must Know Facts For Your Next Test

1. The secant function has vertical asymptotes where $\cos(\theta) = 0$, which occur at $\theta = \frac{(2k+1)\pi}{2}$ for any integer $k$.
2. The range of the secant function is $(-\infty, -1] \cup [1, \infty)$.
3. The period of the secant function is $2\pi$, meaning it repeats every $2\pi$ units.
4. The graph of the secant function consists of segments that are upward or downward facing curves between its asymptotes.
5. The secant function is undefined at points where the cosine function equals zero.

Review Questions

• What is the relationship between the secant and cosine functions?
• Where are the vertical asymptotes located in the graph of the secant function?
• What is the period of the secant function?

Related terms

Cosine Function: $\cos(\theta)$, a trigonometric function representing the x-coordinate of a point on the unit circle.

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

Tangent Function: $\tan(\theta)$, a trigonometric function defined as $ \frac{ \sin ( \theta ) } { \cos ( \theta ) }$.