Solve a sin θ = b (0° ≤ θ ≤ 360°)
A standard method from Trigonometry (2-D): the steps and worked examples.
Steps
- Make sin θ the subject.
- Find the reference angle α with the calculator, using the positive value.
- Use ASTC to choose the quadrants where the sign is correct.
- Write each answer: Quadrant II → 180° − α; III → 180° + α; IV → 360° − α.
Worked examples
Example 1: Solve 5 sin θ + 3 = 0 for 0° ≤ θ ≤ 360°.
sin θ = −0.6
reference angle α = sin⁻¹(0.6) ≈ 36.87°
sin is negative in quadrants III and IV
θ ≈ 180° + 36.87° = 216.9° or θ ≈ 360° − 36.87° = 323.1°For the whole topic, read Trigonometry (2-D): key points, common mistakes and how the DSE tests it.