Solve the equation sec θcos(θ – 60°) = 4 for −180° < θ < 180°.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [M1] Attempt to express equation in terms of cosθ and sinθ only, using a correct identity and secθ= 1/cosθ
2. [A1] Obtain cosθcos60 + sinθsin60 = 4cosθ OE
3. [M1] Either divide by cosθ to find value of tanθ or use another correct method to find sinθ or cosθ May still involve cos60 and sin 60.
4. [A1] Obtain tanθ = 7/√3 or tanθ=4.04... or sinθ = 7/√52 or sinθ=0.970... or cosθ = √3/√52 or cosθ=0.240...
5. [A1] Obtain -103.9 and 76.1 Or greater accuracy; and no others between –180 and 180.