Express the equation 7 tan θ + 4 cot θ – 13 sec θ = 0 in terms of sin θ only.

Mark scheme

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

1. [1] Attempt to express left hand side of the equation in terms of sin θ and cos θ with at least two of the terms correct and no missing θs Condone use of x instead of θ
2. [1] Obtain 7 sin² θ + 4cos² θ – 13sin θ [=0] SOI, OE
3. [1] Obtain 3sin² θ – 13sin θ + 4 = 0 Allow if missing θs are recovered
4. [1] Attempt solution of 3-term quadratic equation for sin θ
5. [1] Obtain sin θ = 1/3 and hence 19.5 or greater accuracy
6. [1] Obtain second value 160.5 or greater accuracy; and no other values within the given range FT on 180° - their 19.5°