OCR MEI C2 2006 June — Question 3 3 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2006
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard trigonometric equations
TypeFunction properties and inverses
DifficultyModerate -0.8 This is a straightforward application of the Pythagorean identity to find cos θ, then dividing to get tan θ. It requires only basic trigonometric identities and simple arithmetic with surds, making it easier than average but not trivial due to the exact value requirement.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1

\(\theta\) is an acute angle and \(\sin \theta = \frac{1}{4}\). Find the exact value of \(\tan \theta\). [3]

AnswerMarks Guidance
\(1/\sqrt{15}\) i.s.w. not \(+/-\)\(3\) M2 for \(\sqrt{15}\) seen; M1 for rt angled triangle with side 1 and hyp 4, or \(\cos^2 \theta = 1 - 1/4 \cdot^2\)
$1/\sqrt{15}$ i.s.w. not $+/-$ | $3$ | M2 for $\sqrt{15}$ seen; M1 for rt angled triangle with side 1 and hyp 4, or $\cos^2 \theta = 1 - 1/4 \cdot^2$ | $3$ |
$\theta$ is an acute angle and $\sin \theta = \frac{1}{4}$. Find the exact value of $\tan \theta$. [3]

\hfill \mbox{\textit{OCR MEI C2 2006 Q3 [3]}}