Solve the equation sec θ = 5 cosec θ for 0° < θ < 360°.

Mark scheme

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

1. [B1] Use secθ = 1/cosθ and cosecθ = 1/sinθ or other appropriate identities Must be using sec²θ = 1 + tan²θ and cosec²θ = 1 + cot²θ.
2. [M1] Obtain tanθ = k using correct identities OE For any non-zero constant k, if using other identities, must come from a 3-term quadratic equation.
3. [A1] Obtain tanθ = 5 and hence 78.7° AWRT
4. [A1] Obtain 258.7° and no other solutions in the range AWRT