Express 4 cos x − sin x in the form Rcos(x + α), where R > 0 and 0° < α < 90°. State the exact value of R and give α correct to 2 decimal places.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [B1] (a) State R = √17
2. [M1] (a) Use correct trig formulae to find α (Correct expansion and correct expression for trig ratio for α)
3. [A1] (a) Obtain α = 14.04°
4. [B1 FT] (b) Evaluate cos⁻¹(3/√17) to at least 1 d.p. (43.3138...°)
5. [M1] (b) Use correct method to find a value of x in the interval
6. [A1] (b) Obtain answer, e.g. 14.6°
7. [M1] (b) Use a correct method to find a second answer in the interval
8. [A1] (b) Obtain second answer in the interval, e.g. 151.3°, and no other in the interval