Moderate -0.3 This is a standard trigonometric equation requiring the identity sin²θ = 1 - cos²θ to convert to a quadratic in cos θ, then solving the resulting quadratic. It's a routine textbook exercise with clear steps (substitute identity, rearrange to standard form, solve quadratic, find angles in given range), making it slightly easier than average but still requiring multiple techniques.
Use of \(s^2+c^2=1\) to eliminate sine. Correct equation
M1 A1
\(\cos\theta = 0, \theta = 90°\)
B1
Co.
or \(\cos\theta = -\frac{2}{3}, \theta = 131.8°\)
A1
Co. (to 1 d.p or more – there must be only this answer in the range 0 to 180))
(i) $3\sin^2\theta - 2\cos\theta - 3 = 0$
Use of $s^2+c^2=1$ to eliminate sine. Correct equation | M1 A1 |
$\cos\theta = 0, \theta = 90°$ | B1 | Co.
or $\cos\theta = -\frac{2}{3}, \theta = 131.8°$ | A1 | Co. (to 1 d.p or more – there must be only this answer in the range 0 to 180)) | [4]