OCR C4 — Question 4 7 marks

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard trigonometric equations
TypeMixed sin and cos linear
DifficultyModerate -0.3 This is a slightly below-average A-level question. Part (i) requires expanding sin(θ+45°) using the addition formula and manipulating to find tan θ, which is straightforward with clear guidance. Part (ii) is routine inverse tangent calculation. The question telegraphs the method and requires only standard techniques without problem-solving insight.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals

The angle \(\theta\) satisfies the equation \(\sin(\theta + 45°) = \cos\theta\).
  1. Using the exact values of \(\sin 45°\) and \(\cos 45°\), show that \(\tan\theta = \sqrt{2} - 1\). [5]
  2. Find the values of \(\theta\) for \(0° < \theta < 360°\). [2]

The angle $\theta$ satisfies the equation $\sin(\theta + 45°) = \cos\theta$.

\begin{enumerate}[label=(\roman*)]
\item Using the exact values of $\sin 45°$ and $\cos 45°$, show that $\tan\theta = \sqrt{2} - 1$. [5]
\item Find the values of $\theta$ for $0° < \theta < 360°$. [2]
\end{enumerate}

\hfill \mbox{\textit{OCR C4  Q4 [7]}}