Standard +0.3 This is a standard reciprocal trig equation requiring the Pythagorean identity (1 + cot²θ = cosec²θ) to convert to a quadratic in cosecθ, then solving and finding angles. It's slightly above average difficulty due to reciprocal functions being less familiar than sin/cos, but follows a routine procedure with no novel insight required.
Use trig identity correctly to obtain a quadratic in \(\cosec \theta\) or \(\sin \theta\)
M1
Solve the quadratic correctly
M1
Obtain \(\sin \theta = \frac{3}{4}\) or \(-\frac{3}{4}\)
A1
Obtain one correct answer
A1
Carry out correct method for second answer from either root
DM1
Obtain remaining 3 answers from 14.5, 165.5, 221.8, 318.2 and no others in the range [Ignore answers outside the given range]
A1
[6]
Use trig identity correctly to obtain a quadratic in $\cosec \theta$ or $\sin \theta$ | M1 |
Solve the quadratic correctly | M1 |
Obtain $\sin \theta = \frac{3}{4}$ or $-\frac{3}{4}$ | A1 |
Obtain one correct answer | A1 |
Carry out correct method for second answer from either root | DM1 |
Obtain remaining 3 answers from 14.5, 165.5, 221.8, 318.2 and no others in the range [Ignore answers outside the given range] | A1 | [6]