| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Find exact trigonometric values |
| Difficulty | Moderate -0.3 This is a straightforward application of the addition formula for sine. Part (i) requires expanding sin(x+30°) and sin(x-30°) using the standard formula, then simplifying—a routine algebraic exercise. Part (ii) is a direct substitution (x=45°) requiring only recall of sin 45°=1/√2. The question tests standard technique with minimal problem-solving, making it slightly easier than average for C3. |
| Spec | 1.05g Exact trigonometric values: for standard angles1.05l Double angle formulae: and compound angle formulae |
\begin{enumerate}
\item (i) Show that
\end{enumerate}
$$\sin ( x + 30 ) ^ { \circ } + \sin ( x - 30 ) ^ { \circ } \equiv a \sin x ^ { \circ }$$
where $a$ is a constant to be found.\\
(ii) Hence find the exact value of $\sin 75 ^ { \circ } + \sin 15 ^ { \circ }$, giving your answer in the form $b \sqrt { 6 }$.\\
\hfill \mbox{\textit{OCR C3 Q1 [6]}}