Moderate -0.8 This is a straightforward application of the Pythagorean identity cos²θ + sin²θ = 1. Students substitute the given value, rearrange to find cos²θ = 1 - 3/16 = 13/16, then take the square root to get ±√13/4. It requires only one standard identity and basic algebraic manipulation, making it easier than average.
B2 for \(-\frac{\sqrt{13}}{4}\) or \(\frac{\sqrt{13}}{16}\) or M1 for \(\sqrt{13}\) or \(\sin^2\theta + \cos^2\theta = 1\) used
Question 1:
$\pm\frac{\sqrt{13}}{4}$ | 3 | B2 for $-\frac{\sqrt{13}}{4}$ or $\frac{\sqrt{13}}{16}$ or M1 for $\sqrt{13}$ or $\sin^2\theta + \cos^2\theta = 1$ used | 3
1 Given that $\sin \theta = \frac { \sqrt { 3 } } { 4 }$, find in surd form the possible values of $\cos \theta$.
\hfill \mbox{\textit{OCR MEI C2 Q1 [3]}}