Sine function

Definition

The sine function, denoted as $\sin(\theta)$, relates the angle $\theta$ in a right triangle to the ratio of the length of the opposite side to the hypotenuse. It is a periodic function with a period of $2\pi$.

5 Must Know Facts For Your Next Test

1. $\sin(0) = 0$, $\sin(\pi/2) = 1$, $\sin(\pi) = 0$, and $\sin(3\pi/2) = -1$.
2. The sine function has an amplitude of 1, meaning it oscillates between -1 and 1.
3. The unit circle definition: for any angle $\theta$, $\sin(\theta)$ is the y-coordinate of the point where the terminal side of the angle intersects the unit circle.
4. Sine is an odd function, satisfying $\sin(-x) = -\sin(x)$.
5. The graph of the sine function is a smooth, continuous wave that repeats every $2 \pi$.

Review Questions

• What is the value of $ \sin( \pi/4 )$?
• Explain why sine is considered an odd function.
• How does the unit circle help in understanding the sine function?

Related terms

Cosine Function: The cosine function, denoted as $ \cos ( \theta ) $, relates an angle in a right triangle to the ratio of the adjacent side to the hypotenuse.

Unit Circle: A circle with a radius of 1 centered at the origin on a coordinate plane; used to define trigonometric functions.

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