Find Trig Function Values Given the Tangent Value and the Sine Function is Positive

Given the tangent of angle theta is -1/2 and that the sine of theta is positive, find all 5 remaining trigonometric functions for this angle. Initially the signs of the tangent and the sine functions are used to determine that angle theta terminates in QII. A sketch is drawn of the angle and the values of x and y are identified from the value of the tangent function. These values along with the Pythagorean Theorem are 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
0:30 Find Quadrant for Angle
2:22 Draw Theta in QII
3:15 Find x, y and r
4:57 Find 5 Other Trig Functions