A-LevelMathematicsTrigonometry9709/31 · Oct/Nov 2025 · Q38 Marks
Express 3√2sin(x+45°) + cosx in the form Rcos(x−α), where R > 0 and 0° < α < 90°.
- (a)Express 3√2sin(x+45°) + cosx in the form Rcos(x−α), where R > 0 and 0° < α < 90°.[4]
- (b)Hence solve the equation 3√2sin(3θ+45°) + cos3θ = -4 for 0° < θ < 180°.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [B1] Obtain 3sinx + 4cosx
- [B1 FT] State R = 5
- [M1] Use trig formula to find α e.g. α = tan⁻¹ (3/4)
- [A1] Obtain α=36.9° (or awrt 36.9°)
- [B1 FT] Evaluate cos⁻¹ (-4/R)
- [M1] Carry out a correct method to find a value of θ in the given interval
- [A1] Obtain answer, e.g. 60(.0)°
- [A1] Obtain a second answer, e.g. 84.6° and no other in the interval
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