OCR MEI C2 2007 January — Question 3 3 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2007
SessionJanuary
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTrig Graphs & Exact Values
TypeFind exact trig values from given ratio
DifficultyModerate -0.8 This is a straightforward application of Pythagoras' theorem to find the opposite side from the given adjacent/hypotenuse ratio, then calculating tan θ = opposite/adjacent. It requires only basic trigonometric definitions and one calculation step, making it easier than average but not trivial since exact form (√8/1 = 2√2) is required.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1
3 Given that \(\cos \theta = \frac { 1 } { 3 }\) and \(\theta\) is acute, find the exact value of \(\tan \theta\).
Question 3:
AnswerMarks Guidance
\(\sin\theta = \frac{\sqrt{8}}{3}\) or \(\frac{2\sqrt{2}}{3}\)M1 A1 Using \(\sin^2\theta + \cos^2\theta = 1\)
\(\tan\theta = \frac{\sqrt{8}}{1} = 2\sqrt{2}\)A1 Accept \(\frac{2\sqrt{2}}{1}\); exact form required 
## Question 3:
$\sin\theta = \frac{\sqrt{8}}{3}$ or $\frac{2\sqrt{2}}{3}$ | M1 A1 | Using $\sin^2\theta + \cos^2\theta = 1$
$\tan\theta = \frac{\sqrt{8}}{1} = 2\sqrt{2}$ | A1 | Accept $\frac{2\sqrt{2}}{1}$; exact form required

---
3 Given that $\cos \theta = \frac { 1 } { 3 }$ and $\theta$ is acute, find the exact value of $\tan \theta$.

\hfill \mbox{\textit{OCR MEI C2 2007 Q3 [3]}}
This paper (13 questions)
View full paper
Q1 2 Q2 3 Q3 3 Q4 3 Q5 5 Q6 4 Q7 3 Q8 5 Q9 4 Q10 4 Q11 12 Q12 12 Q13 12