OCR MEI C2 — Question 4 3 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicQuadratic trigonometric equations
TypeDirect solve: tanθ equation factorisation
DifficultyModerate -0.3 This is a straightforward trigonometric equation that simplifies immediately to sin θ = √3/2 using the identity tan θ = sin θ/cos θ. Students then recall standard angles (60° and 120°) from the unit circle. It requires basic algebraic manipulation and knowledge of special angles, making it slightly easier than average but not trivial since it involves recognizing the simplification and finding two solutions in the given range.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals
4 Find the values of \(\theta\) such that \(0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }\) which satisfy the equation $$\cos \theta \tan \theta = \frac { \sqrt { 3 } } { 2 }$$
AnswerMarks Guidance
Cancellation of \(\cos\theta \Rightarrow \cos\theta\frac{\sin\theta}{\cos\theta} = \sin\theta\) \(\Rightarrow \theta = 60°, 120°\)M1 A1 A1 3 marks 
Cancellation of $\cos\theta \Rightarrow \cos\theta\frac{\sin\theta}{\cos\theta} = \sin\theta$ $\Rightarrow \theta = 60°, 120°$ | M1 A1 A1 | 3 marks
4 Find the values of $\theta$ such that $0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }$ which satisfy the equation

$$\cos \theta \tan \theta = \frac { \sqrt { 3 } } { 2 }$$

\hfill \mbox{\textit{OCR MEI C2  Q4 [3]}}
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Q1 5 Q2 4 Q3 4 Q4 3 Q5 5 Q6 5 Q7 5 Q8 5 Q9 12 Q10 12 Q11 12