Solving trig equations
Find all solutions in a stated range. Use CAST or sketches; remember periodic solutions.
Find principal value with arcsin/arccos/arctan; then add/subtract multiples of 360° (or 2π) and use symmetry to find others in the range.
Worked examples
sin x = 0.5, 0° ≤ x < 360°: x = 30, 150.
cos 2x = ½, 0 ≤ x < π: 2x = π/3, 5π/3 ⇒ x = π/6, 5π/6.
tan x = −1: x = 135, 315 in 0-360°.
Frequently asked questions
CAST diagram?
C (cos), A (all), S (sin), T (tan) labelling the four quadrants where each is positive.
Multiple-angle equations?
Adjust the range first. cos 2x in 0 ≤ x < π means 2x in 0 ≤ 2x < 2π.