A-LevelMathematicsTrigonometry9709/22 · May/June 2022 · Q89 Marks
Express 3 sin 2θ sec θ + 10 cos(θ – 30°) in the form R sin(θ+ α) where R > 0 and 0° < α < 90°. Give the value of α correct to 2 decimal places.
- (a)Express 3 sin 2θ sec θ + 10 cos(θ – 30°) in the form R sin(θ+ α) where R > 0 and 0° < α < 90°. Give the value of α correct to 2 decimal places.[6]
- (b)Hence solve the equation 3 sin 4β sec 2β + 10 cos(2β – 30°) = 2 for 0° < β < 90°.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] Use sin 2θ = 2 sin θ cos θ and sec θ = 1/cos θ to obtain 6 sin θ
- [B1] Expand second term to obtain 5√3 cos θ + 5 sin θ
- [B1] Simplify to obtain 11 sin θ + 5√3 cos θ
- [B1] State R=14 FT their k₁ cosθ + k₂ sinθ
- [M1] Use appropriate trigonometry to find α
- [A1] Obtain α = 38.21 AWRT
- [B1] State or imply 14sin(2β+38.21) = 2 FT their R and α
- [M1] Carry out correct process to find value of β between 0° and 90°
- [A1] Obtain 66.8 AWRT
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