A-LevelMathematicsTrigonometry9709/33 · May/June 2022 · Q25 Marks
Solve the equation cos(θ – 60°) = 3 sin θ, for 0° ≤ θ ≤ 360°.
- Solve the equation cos(θ – 60°) = 3 sin θ, for 0° ≤ θ ≤ 360°.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] Use correct cos(A−B) formula to obtain an equation in cosθ and sinθ
- [M1] Use trigonometric formula and substitute values for cos 60 and sin 60 to obtain an equation in tanθ (or cosθ or sinθ)
- [A1] Obtain tan θ = 1/(6−√3) or tan θ = (6+√3)/33 or 0.2343, or cos θ = (3√3)/(√10−3√3) or 0.9736 or sin θ = 1/(√10−3√3) or 0.2281
- [A1] Obtain answer, e.g. θ = 13.2°
- [A1 FT] Obtain second answer, e.g. θ = 193.2° and no others in the given interval
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