Period

Definition

The period of a trigonometric function is the interval over which it completes one full cycle and starts to repeat. For sine and cosine functions, the period is $2\pi$.

5 Must Know Facts For Your Next Test

1. The period of $\sin(x)$ and $\cos(x)$ is $2\pi$.
2. To find the period of functions like $A \sin(Bx + C) + D$, use the formula $\frac{2\pi}{|B|}$.
3. For tangent and cotangent functions, the period is $\pi$.
4. Graphically, the period can be observed as the distance between repeating points on the x-axis.
5. Identifying the period helps in sketching accurate graphs of trigonometric functions.

Review Questions

• What is the period of $y = \sin(3x)$?
• How do you determine the period of a function like $y = A \cos(Bx + C) + D$?
• What role does the coefficient B play in determining the period of a sine or cosine function?

Related terms

Amplitude: The height from the centerline to the peak (or trough) of a wave.

$\sin(x)$: $\sin(x)$ is a periodic function with a fundamental period of $2\pi$.

$\cos(x)$: $\cos(x)$ is a periodic function with a fundamental period of $2\pi$.