Theory question 104
TrigonometrySolve 3cos 2x − sin x = 0 for 0° ≤ x ≤ 360°.
Show the model answer
Model answer
cos 2x = 1 − 2sin²x: 3 − 6sin²x − sin x = 0, i.e. 6sin²x + sin x − 3 = 0.
sin x = (−1 ± √73)/12 = 0.6287 or −0.7953.
sin x = 0.6287: x = 38.95°, 141.05°.
sin x = −0.7953: x = 232.69°, 307.31°.
x ≈ 39.0°, 141.0°, 232.7°, 307.3°.
Explanation
Write cos 2x in terms of sin x to get a quadratic in sin x.