Moderate -0.3 This is a straightforward double angle equation requiring substitution of cos 2θ = 2cos²θ - 1, leading to a quadratic in cos θ. The algebra is routine and the interval restriction makes finding solutions simpler than a full 360° range. Slightly easier than average due to limited steps and standard technique.
Use correct trig formula (or formulae) and obtain an equation in \(\cos\theta\)
M1
Obtain \(8\cos^2\theta + \cos\theta - 7 = 0\), or equivalent
A1
Solve a 3-term quadratic in \(\cos\theta\) and reach \(\theta = \cos^{-1}(a)\)
M1
Obtain answer \(29.0°\)
A1
Obtain answer \(180°\) and no others
A1
[5]
[Ignore answers outside the given interval. Treat answers in radians (0.505 and 3.14 or \(\pi\)) as a misread.]
[SR: The answer \(180°\) found by inspection can earn B1.]
Use correct trig formula (or formulae) and obtain an equation in $\cos\theta$ | M1 |
Obtain $8\cos^2\theta + \cos\theta - 7 = 0$, or equivalent | A1 |
Solve a 3-term quadratic in $\cos\theta$ and reach $\theta = \cos^{-1}(a)$ | M1 |
Obtain answer $29.0°$ | A1 |
Obtain answer $180°$ and no others | A1 | [5]
[Ignore answers outside the given interval. Treat answers in radians (0.505 and 3.14 or $\pi$) as a misread.]
[SR: The answer $180°$ found by inspection can earn B1.]