In radians, a full turn is 2π. The second solutions use π instead of 180°: for sin x, use π − α; for cos x, use 2π − α; for tan x, add π.
For a compound angle like tan(x + π/6) = −√3, first change the interval: if 0 ≤ x < 2π, then π/6 ≤ x + π/6 < 13π/6. Solve for x + π/6 in that interval (2π/3 and 5π/3), then subtract π/6 to get x = π/2 and 3π/2.
Worked example
Solve sin²x − sin x = 0 for 0° ≤ x < 360°.
- Factorise: sin x(sin x − 1) = 0.
- sin x = 0 gives 0°, 180°; sin x = 1 gives 90°.
Answer:x = 0°, 90° or 180°
Key words
- compound angle
- an angle like x + π/6
- exact answer
- in terms of π
- adjust the interval
- shift the range for a compound angle
Practise this
New questions every time.
Common Core-referenced: HSF-TF.B.7