9 Showing your method, solve the equation \(2 \sin ^ { 2 } \theta = \cos \theta + 2\) for values of \(\theta\) between \(0 ^ { \circ }\) and \(360 ^ { \circ }\).
Show mark scheme
Show mark scheme source
Question 9:
Answer Marks
Guidance
Answer/Working Mark
Guidance
\(2(1-\cos^2\theta) = \cos\theta + 2\) M1
for \(1-\cos^2\theta = \sin^2\theta\) substituted
\(-2\cos^2\theta = \cos\theta\) s.o.i. A1
graphic calc method: allow M3 for intersection of \(y = 2\sin^2\theta\) and \(y = \cos\theta + 2\) and A2 for all four roots
Valid attempt at solving their quadratic in \(\cos\theta\) DM1
\(\cos\theta = -\frac{1}{2}\) www A1
All four answers correct but unsupported scores B2. 120 and 240 only: B1
\(\theta = 90, 270, 120, 240\) A1
Copy
## Question 9:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $2(1-\cos^2\theta) = \cos\theta + 2$ | M1 | for $1-\cos^2\theta = \sin^2\theta$ substituted |
| $-2\cos^2\theta = \cos\theta$ s.o.i. | A1 | graphic calc method: allow M3 for intersection of $y = 2\sin^2\theta$ and $y = \cos\theta + 2$ and A2 for all four roots |
| Valid attempt at solving their quadratic in $\cos\theta$ | DM1 | |
| $\cos\theta = -\frac{1}{2}$ www | A1 | All four answers correct but unsupported scores B2. 120 and 240 only: B1 |
| $\theta = 90, 270, 120, 240$ | A1 | | 5 |
---
Show LaTeX source
Copy
9 Showing your method, solve the equation $2 \sin ^ { 2 } \theta = \cos \theta + 2$ for values of $\theta$ between $0 ^ { \circ }$ and $360 ^ { \circ }$.
\hfill \mbox{\textit{OCR MEI C2 Q9 [5]}}