Standard +0.3 This is a straightforward reciprocal trig equation that uses the standard identity cosec²θ = 1 + cot²θ to convert to a quadratic in cot θ, then solve and find angles. It requires recall of the identity and basic algebraic manipulation, but follows a standard textbook pattern with no novel insight needed. Slightly easier than average due to its routine nature.
Use correct trig identity to obtain a quadratic in \(\cot\theta\) or \(\tan\theta\)
M1
Solve the quadratic correctly
A1
Obtain \(\tan\theta = \frac{1}{2}\) or \(-\frac{2}{3}\)
A1\(\checkmark\)
Obtain answer \(26.6°\) or \(146.3°\)
A1
Carry out correct method for second answer from either root
M1
Obtain remaining 3 answers from \(26.6°, 146.3°, 206.6°, 326.3°\) and no others in the range [Ignore answers outside the given range]
A1
[6]
Use correct trig identity to obtain a quadratic in $\cot\theta$ or $\tan\theta$ | M1 |
Solve the quadratic correctly | A1 |
Obtain $\tan\theta = \frac{1}{2}$ or $-\frac{2}{3}$ | A1$\checkmark$ |
Obtain answer $26.6°$ or $146.3°$ | A1 |
Carry out correct method for second answer from either root | M1 |
Obtain remaining 3 answers from $26.6°, 146.3°, 206.6°, 326.3°$ and no others in the range [Ignore answers outside the given range] | A1 | [6]