Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2. 84°

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. Understanding this concept is crucial for determining the location of the terminal side of the angle and subsequently the signs of the trigonometric functions.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants, each defined by the signs of the x and y coordinates. In Quadrant I, both x and y are positive; in Quadrant II, x is negative and y is positive; in Quadrant III, both are negative; and in Quadrant IV, x is positive and y is negative. The quadrant in which the terminal side of the angle lies determines the signs of the sine, cosine, and tangent functions.

Signs of Trigonometric Functions

The signs of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) depend on the quadrant in which the angle's terminal side is located. In Quadrant I, all functions are positive; in Quadrant II, sine and cosecant are positive; in Quadrant III, tangent and cotangent are positive; and in Quadrant IV, cosine and secant are positive. This knowledge is essential for accurately determining the values of these functions for any given angle.