Solve in radians on 0≤θ≤2π.

01 / Standard#Your turn

\sqrt3\cos\theta-\sin\theta=-1

Official paper · jm01-2022 · II.4(b) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use part (a) to obtain cos(θ+π/6)=−1/2.

Hint 2

Shift the argument interval before selecting the angles.

Worked solution

θ=π/2 or 7π/6.

Checks and common pitfalls: Both cosine solutions must be retained.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The shifted angle is in [π/6,13π/6].
$\theta+\pi/6=2\pi/3\text{ or }4\pi/3$
Subtract the phase.
$\theta=\pi/2\text{ or }7\pi/6$

Think first. Reveal a hint when the class is ready.

2022 JM01