Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2. ―15°

Key Concepts

Standard Position of an Angle

An angle is in standard position when its vertex is at the origin of a coordinate system and its initial side lies along the positive x-axis. The angle is measured counterclockwise from the initial side. If the angle is negative, as in the case of -15°, it is measured clockwise from the positive x-axis.

Quadrants and Signs of Trigonometric Functions

The coordinate plane is divided into four quadrants, each with specific signs for the trigonometric functions. In Quadrant I, all functions are positive; in Quadrant II, sine is positive; in Quadrant III, tangent is positive; and in Quadrant IV, cosine is positive. Understanding which quadrant an angle lies in helps determine the signs of sine, cosine, and tangent.

Reference Angles

A reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. For negative angles, the reference angle can be found by adding 360° to the angle measure until it is positive. For -15°, the reference angle is 15°, which helps in determining the values of the trigonometric functions based on their signs in the corresponding quadrant.