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

Verified step by step guidance

1. Convert the angle from degrees to a standard position by adding 360° to -270°.
2. Determine the reference angle by finding the positive angle equivalent to the standard position angle.
3. Identify the quadrant in which the angle lies after conversion.
4. Use the reference angle and the quadrant to determine the sign of the sine function.
5. Apply the sine function to the reference angle, considering the sign determined by the quadrant.

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°.