| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2023 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Find exact trigonometric values |
| Difficulty | Standard +0.3 This is a standard trigonometry question covering routine A-level techniques: (a) is direct application of a compound angle formula with given identity, (b) is a standard quadratic-type trig equation using identities, and (c) involves the R-formula method which is a core C2/C3 technique. All parts follow textbook patterns with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.05g Exact trigonometric values: for standard angles1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05l Double angle formulae: and compound angle formulae1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc |
\begin{enumerate}[label=(\alph*)]
\item Using the trigonometric identity $\cos(A + B) = \cos A \cos B - \sin A \sin B$, show that the exact value of $\cos 75°$ is $\frac{\sqrt{6} - \sqrt{2}}{4}$. [3]
\item Solve the equation $2\cot^2 x + \cosec x = 4$ for values of $x$ between $0°$ and $360°$. [6]
\item \begin{enumerate}[label=(\roman*)]
\item Express $7\cos\theta - 24\sin\theta$ in the form $R\cos(\theta + \alpha)$, where $R$ and $\alpha$ are constants with $R > 0$ and $0° < \alpha < 90°$.
\item Find all values of $\theta$ in the range $0° < \theta < 360°$ satisfying
$$7\cos\theta - 24\sin\theta = 5.$$ [6]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2023 Q6 [15]}}