Solve Trigonometric Equations

Introduction

There are 3 + 1 steps to solving the basic trigonometric equation of the forms:

• sin x = k

• cos x = k

• tan x = k

for 0° < x <360°.

Step 1: Find the basic angle / reference angle (α), arcsin(|k|) or arccos(|k|) or arctan(|k|).

Step 2: Use ASTC to determine the 2 quadrants that the angle is in.

Step 3: Evaluate the respective angles.

• 1st Quadrant = α

• 2nd Quadrant = 180° - α

• 3rd Quadrant = 180° + α

• 4th Quadrant = 360° - α

Checkback! Lastly, you should substitute your answers back into the equation to verify your solution.