A-LevelMathematicsTrigonometry9709/32 · Feb/Mar 2021 · Q58 Marks
Express √7 sin x + 2 cos x in the form R sin(x + α), where R > 0 and 0° < α < 90°. State the exact value of R and give α correct to 2 decimal places. Hence solve the equation √7 sin 2θ + 2 cos 2θ = 1, for 0° < θ < 180°.
- (a)Express √7 sin x + 2 cos x in the form R sin(x + α), where R > 0 and 0° < α < 90°. State the exact value of R and give α correct to 2 decimal places.[3]
- (b)Hence solve the equation √7 sin 2θ + 2 cos 2θ = 1, for 0° < θ < 180°.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.
- [B1] State R = √11
- [M1] Use trig formulae to find α
- [A1] Obtain α = 37.09°
- [B1 FT] Evaluate sin⁻¹(1/√11) to at least 2 dp (17.5484°)
- [M1] Use correct method to find a value of θ in the interval
- [A1] Obtain answer, e.g. 62.7°
- [M1] Use a correct method to obtain a second answer
- [A1] Obtain second answer, e.g. 170.2°, and no other in the interval
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