Find Trig Function Values Given the Tangent Value and Quadrant of Angle

Given tan(theta) = -5/2 and theta terminates in QIV, find the five remaining trigonometric functions. A sketch is drawn of the angle in quadrant IV and the values of y and x are identified from the value of the tangent function as tan(theta)=y/x. The Pythagorean Theorem is used to find the value of r. Once x, y, and r are known, then sin(theta)=y/r and cos(theta)=x/r. The cosecant, secant, and cotangent values are found using their definitions in terms of reciprocal functions: cot(theta)=1/tan(theta), csc(theta)=1/sin(theta), and sec(theta)=1/cos(theta).

Timestamps
0:00 Introduction
0:39 Draw Theta in QIV
1:18 Find x, y and r
3:00 Find 5 Other Trig Functions
5:25 Rationalize the Denominators