Find the indicated function value. If it is undefined, say so. See Example 4. sin(―270°)

Key Concepts

Unit Circle

The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It is fundamental in trigonometry as it provides a geometric interpretation of the sine, cosine, and tangent functions. Angles are measured from the positive x-axis, and the coordinates of points on the circle correspond to the values of these trigonometric functions.

Sine Function

The sine function, denoted as sin(θ), represents the y-coordinate of a point on the unit circle corresponding to an angle θ. It is periodic with a period of 360° (or 2π radians), meaning that sin(θ) = sin(θ + 360°n) for any integer n. Understanding the sine function is crucial for evaluating trigonometric values at various angles, including negative angles.

Negative Angles

Negative angles in trigonometry indicate a clockwise rotation from the positive x-axis. For example, an angle of -270° corresponds to a 270° rotation in the clockwise direction. This concept is important for determining the sine value of angles that exceed 360° or are negative, as it allows us to find equivalent angles within the standard range of 0° to 360°.