Solving Basic Trigonometric Equations
When solving trig equations, we need to find all angles that make the equation true within a specific range. For example, when solving sine equations like sinθ = -1/2, we first identify which quadrants have negative sine values (quadrants III and IV).
To find all solutions, we locate the reference angle first. If sinθ = -1/2, we know that sin(30°) = 1/2, so our reference angle is 30°. Then we place this angle in the correct quadrants: 210° in quadrant III and 330° in quadrant IV .
For tangent equations like tanθ = -1/√3, we follow a similar approach. Since tangent is negative in quadrants II and IV, and the reference angle where tan(30°) = 1/√3, our solutions are 210° and 330°.
Pro Tip: Always check which quadrants your trig function is positive or negative in! Sine is positive in I and II, negative in III and IV. Tangent is positive in I and III, negative in II and IV.
