A-LevelMathematicsTrigonometry9709/32 · May/June 2020 · Q57 Marks
Express √2 cos x – √5 sin x in the form Rcos(x + α), where R > 0 and 0° < α < 90°. Give the exact value of R and the value of α correct to 3 decimal places.
- (a)Express √2 cos x – √5 sin x in the form Rcos(x + α), where R > 0 and 0° < α < 90°. Give the exact value of R and the value of α correct to 3 decimal places.[3]
- (b)Hence solve the equation √2 cos 2θ – √5 sin 2θ = 1, for 0° < θ < 180°.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B1] State R = √7
- [M1] Use trig formulae to find α
- [A1] Obtain α = 57.688°
- [B1 FT] Evaluate cos⁻¹(1/√7) to at least 3 d.p. (67.792°) (FT is on their R)
- [M1] Use correct method to find a value of θ in the interval
- [A1] Obtain answer, e.g. 5.1°
- [A1] Obtain second answer, e.g. 117.3°, only
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