Cosine function

Definition

The cosine function, denoted as $\cos(\theta)$, is a trigonometric function that represents the x-coordinate of a point on the unit circle at an angle $\theta$ from the positive x-axis. It is periodic with a period of $2\pi$ and ranges from -1 to 1.

5 Must Know Facts For Your Next Test

1. The cosine function is even, meaning $\cos(-\theta) = \cos(\theta)$.
2. The maximum value of $\cos(\theta)$ is 1 and occurs at multiples of $2\pi$.
3. The minimum value of $\cos(\theta)$ is -1 and occurs at odd multiples of $\pi$.
4. The cosine function has zeros at $(2n+1) \frac{\pi}{2}$ where n is an integer.
5. In the unit circle, $\cos(0) = 1$, which corresponds to the point (1,0).

Review Questions

• What is the period of the cosine function?
• At what angles does the cosine function achieve its maximum value?
• How does the symmetry property of the cosine function affect its graph?

Related terms

Unit Circle: A circle with a radius of one centered at the origin in the coordinate plane. It is used to define trigonometric functions.

Periodic Function: A function that repeats its values in regular intervals or periods.

Sine Function: $\sin(\theta)$ represents the y-coordinate of a point on the unit circle at an angle $\theta$ from the positive x-axis.