A-LevelMathematicsTrigonometry9709/31 · May/June 2017 · Q88 Marks
By first expanding 2 sin(x – 30°), express 2 sin(x – 30°) – cosx in the form R sin(x – α), where R > 0 and 0° < α < 90°. Give the exact value of R and the value of α correct to 2 decimal places.
- (i)By first expanding 2 sin(x – 30°), express 2 sin(x – 30°) – cosx in the form R sin(x – α), where R > 0 and 0° < α < 90°. Give the exact value of R and the value of α correct to 2 decimal places.[5]
- (ii)Hence solve the equation 2 sin(x - 30°) – cosx = 1, for 0° < x < 180°.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- Use sin(A - B) formula and obtain an expression in terms of sin x and cos x M1
- Collect terms and reach √3 sin x – 2 cos x, or equivalent A1
- Obtain R = √7 A1
- Use trig formula to find α M1
- Obtain α = 49.11° with no errors seen A1
- Evaluate sin⁻¹(1/√7) to at least 1 d.p. (22.21° to 2 d.p.) B1 FT
- Use a correct method to find a value of x in the interval 0° < x < 180° M1
- Obtain answer 71.3° A1 [ignore answers outside given range.]
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