A-LevelMathematicsTrigonometry9709/32 · Oct/Nov 2019 · Q47 Marks
The context for the parts is: Express (√6) sin x + cos x in the form R sin(x + α), where R > 0 and 0° < α < 90°. Hence solve an equation.
- (i)Express (√6) sin x + 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 3 decimal places.[3]
- (ii)Hence solve the equation (√6) sin 2θ + cos 2θ = 2, for 0° < θ < 180°.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [B1] State R = √7
- [M1] Use correct trig formulae to find α
- [A1] Obtain α = 22.208°
- [B1FT] Evaluate sin⁻¹(2/√7) to at least 1 d.p.
- [M1] Use correct method to find a value of θ in the interval
- [A1] Obtain answer, e.g. 13.4°
- [A1] Obtain second answer, e.g. 54.3° and no extras in the given interval
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →