Moderate -0.3 This is a straightforward trigonometric equation requiring rewriting tan θ as sin θ/cos θ, factoring out sin θ, and solving sin θ = 0 or cos θ = 1/2. It's slightly easier than average as it uses standard techniques with no conceptual surprises, though students must remember to find all solutions in the given range.
may be implied by \(2\cos \theta - 1 = 0\) or better
\(2\cos \theta - 1 = 0\) and \(\sin \theta = 0\)
A1
\([\theta =] 0, 180, 360,\)
B1
\([\theta =] 60, 300\)
B1
or, if to advantage of candidate: B4 for all 5 correct; B3 for 4 correct; B2 for 3 correct; B1 for 2 correct
if 4 marks awarded, lose 1 mark for extra values in the range, ignore extra values outside the range
if extra value(s) in range, deduct one mark from total; do not award if values embedded in trial and improvement approach
$\frac{\sin \theta}{\cos \theta} = 2 \sin \theta$ | M1 | may be implied by $2\cos \theta - 1 = 0$ or better
$2\cos \theta - 1 = 0$ and $\sin \theta = 0$ | A1 |
$[\theta =] 0, 180, 360,$ | B1 |
$[\theta =] 60, 300$ | B1 | or, if to advantage of candidate: B4 for all 5 correct; B3 for 4 correct; B2 for 3 correct; B1 for 2 correct
if 4 marks awarded, lose 1 mark for extra values in the range, ignore extra values outside the range | | if extra value(s) in range, deduct one mark from total; do not award if values embedded in trial and improvement approach