A-LevelMathematicsTrigonometry9709/31 · Oct/Nov 2020 · Q67 Marks
Express √6 cos θ + 3 sin θ in the form R cos(θ – α), where R > 0 and 0° < α < 90°. State the exact value of R and give α correct to 2 decimal places.
- (a)Express √6 cos θ + 3 sin θ in the form R cos(θ – 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 √6 cos (x/3) + 3 sin (x/3) = 2.5, for 0° < x < 360°.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- State R = √15
- Use trig formulae to find α
- Obtain α = 50.77
- Evaluate β = cos⁻¹(2.5/√15) (49.797° to 4 d.p.)
- Use correct method to find a value of x/3 in the interval
- Obtain answer rounding to x = 301.6° to 301.8°
- Obtain second answer rounding to x = 2.9(0)° to 2.9(2)° and no others in the interval
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