Moderate -0.8 This is a straightforward application of the Pythagorean identity cos²θ + sin²θ = 1. Students substitute the given value, solve for cos²θ = 1 - 3/16 = 13/16, then take ±√(13/16) = ±√13/4. It's simpler than average as it requires only one standard identity and basic algebraic manipulation with surds.
\(\pm\sqrt{\frac{13}{4}}\) or \(\pm\frac{\sqrt{13}}{4}\)
B2 for \((-)\sqrt{13}/4\) or \(\pm\sqrt{\frac{13}{16}}\) or M1 for \(\sqrt{13}\) or \(\sin^2\theta + \cos^2\theta = 1\) used
3
$\pm\sqrt{\frac{13}{4}}$ or $\pm\frac{\sqrt{13}}{4}$ | B2 for $(-)\sqrt{13}/4$ or $\pm\sqrt{\frac{13}{16}}$ or M1 for $\sqrt{13}$ or $\sin^2\theta + \cos^2\theta = 1$ used | 3
3 Given that $\sin \theta = \frac { \sqrt { 3 } } { 4 }$, find in surd form the possible values of $\cos \theta$.
\hfill \mbox{\textit{OCR MEI C2 2005 Q3 [3]}}