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; or, if to advantage of candidate: B4 for all 5 correct, B3 for 4 correct, B2 for 3 correct, B1 for 2 correct
\(2\cos\theta - 1 = 0\) and \(\sin\theta = 0\)
A1
\([\theta =]\ 0, 180, 360\)
B1
if extra value(s) in range, deduct one mark from total; do not award if values embedded in trial and improvement approach
\([\theta =]\ 60, 300\)
B1
if 4 marks awarded, lose 1 mark for extra values in the range, ignore extra values outside the range
## Question 6:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{\sin\theta}{\cos\theta} = 2\sin\theta$ | M1 | may be implied by $2\cos\theta - 1 = 0$ or better; or, if to advantage of candidate: B4 for all 5 correct, B3 for 4 correct, B2 for 3 correct, B1 for 2 correct |
| $2\cos\theta - 1 = 0$ and $\sin\theta = 0$ | A1 | |
| $[\theta =]\ 0, 180, 360$ | B1 | if extra value(s) in range, deduct one mark from total; do not award if values embedded in trial and improvement approach |
| $[\theta =]\ 60, 300$ | B1 | if 4 marks awarded, lose 1 mark for extra values in the range, ignore extra values outside the range |