Show that the equation 7 tan θ cos θ + 12 = 0 can be expressed as 12 sin²θ – 7 sin θ – 12 = 0.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [M1*] 7sinθ/cos²θ + 12 = 0 OE Use of tan θ = sin θ / cos θ
2. [DM1] 7sinθ+12(1-sin²θ) [= 0] Use of s² + c² = 1.
3. [A1] → 12sin²θ-7sinθ-12 = 0 AG, WWW Condone use of s, c and t and/or omission of θ throughout working but the A1 is for cao.
4. [M1] [12sin²θ–7sinθ-12 = 0 leading to](4sinθ+3)(3sinθ-4)
5. [B1] sinθ = -3/4 or 4/3 OE, WWW Can be implied by a correct value for sin⁻¹ (-3/4) e.g. -48.6°.
6. [B1] [θ=]228.6°,311.4° AWRT, WWW No others in the range 0°≤θ≤360°. Ignore any answers outside this range. Condone 229°, 311°.