| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Find exact trig values from given ratio |
| Difficulty | Moderate -0.8 This is a straightforward application of Pythagoras to find the adjacent side from sin θ, then calculating tan θ = opposite/adjacent. It requires only basic trig definitions and one algebraic manipulation (√(9-2)/√2 = √7/√2), making it easier than average but not trivial since exact value manipulation is required. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1 |
Question 5:
Right angled triangle with $\sqrt{2}$ on one side and 3 on hypotenuse
Pythagoras used to obtain remaining side $= \sqrt{7}$
M1 for $\tan\theta = \frac{\text{opp}}{\text{adj}} = \frac{\sqrt{2}}{\sqrt{7}}$ or equivalent
A1 for $\cos\theta = \frac{\sqrt{7}}{3}$
M1 for $\cos^2\theta = 1 - \sin^2\theta$ used
A1 for $\cos\theta = \frac{\sqrt{7}}{3}$
A1 for $\tan\theta = \frac{\sin\theta}{\cos\theta} = \frac{\sqrt{2}}{\sqrt{7}}$ or equivalent5 You are given that $\sin \theta = \frac { \sqrt { 2 } } { 3 }$ and that $\theta$ is an acute angle. Find the exact value of $\tan \theta$.
\hfill \mbox{\textit{OCR MEI C2 Q5 [3]}}