A-LevelMathematicsTrigonometry9709/21 · May/June 2018 · Q711 Marks
Express 5 cos θ – 2 sin θ in the form Rcos(θ + α), where R > 0 and 0 < α < ½π. Give the value of α correct to 4 decimal places.
- (i)Express 5 cos θ – 2 sin θ in the form Rcos(θ + α), where R > 0 and 0 < α < ½π. Give the value of α correct to 4 decimal places.[3]
- (ii)Using your answer from part (i), solve the equation 5 cot θ – 4 cosec θ = 2 for 0 < θ < 2π.[5]
- (iii)Find ∫ 1 / (5 cos ½x – 2 sin ½x)² dx.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [B1] State R = √29 or 5.385...
- [M1] Use appropriate trigonometry to find α
- [A1] Obtain 0.3805 with no errors seen
- [B1] State that equation is 5cosθ - 2sinθ = 4
- [M1] Evaluate cos⁻¹(k / R) – α to find one value of θ
- [A1] Obtain 0.353
- [M1] Carry out correct method to find second value
- [A1] Obtain 5.17 and no extra solutions in the range
- [B1 FT] State integrand as (1/R²) sec²(½x + 0.3805)
- [M1] Integrate to obtain form k tan(½x + their α)
- [A1] Obtain (1/ (29 * 1/2)) tan(½x + 0.3805) + c
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