OCR MEI C2 2013 January — Question 9 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2013
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard trigonometric equations
TypeRational trig expressions
DifficultyModerate -0.3 This is a straightforward trigonometric equation requiring basic identity manipulation (tan θ = sin θ/cos θ) to reach a quadratic in sin θ, then solving for standard angles. The algebraic rearrangement is guided by part (i), and the solutions are common angles (30° and 90°). Slightly easier than average due to the scaffolding and routine nature of the techniques.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals

  1. Show that the equation \(\frac{\tan \theta}{\cos \theta} = 1\) may be rewritten as \(\sin \theta = 1 - \sin^2 \theta\). [2]
  2. Hence solve the equation \(\frac{\tan \theta}{\cos \theta} = 1\) for \(0° \leq \theta \leq 360°\). [3]

\begin{enumerate}[label=(\roman*)]
\item Show that the equation $\frac{\tan \theta}{\cos \theta} = 1$ may be rewritten as $\sin \theta = 1 - \sin^2 \theta$. [2]
\item Hence solve the equation $\frac{\tan \theta}{\cos \theta} = 1$ for $0° \leq \theta \leq 360°$. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI C2 2013 Q9 [5]}}