A-LevelMathematicsTrigonometry9709/33 · Oct/Nov 2021 · Q67 Marks
By first expanding cos(x – 60°), show that the expression 2 cos(x - 60°) + cos x can be written in the form R cos(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.
- (a)By first expanding cos(x – 60°), show that the expression 2 cos(x - 60°) + cos x can be written in the form R cos(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]
- (b)Hence find the value of x in the interval 0° < x < 360° for which 2 cos(x – 60°) + cos x takes its least possible value.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [M1] Use cos(A−B) formula and obtain an expression in terms of sin x and cos x
- [A1] Collect terms and reach 2 cos x + √3 sin x
- [A1] State R = √7
- [M1] Use trig formula to find α
- [A1] Obtain α = 40.89°
- [M1] Use correct method to find x
- [A1] Obtain answer x = 220.9°
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