OCR C2 — Question 3 6 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard trigonometric equations
TypeDeduce related solution
DifficultyModerate -0.8 Part (i) is a straightforward rearrangement to show tan θ = 2.5 using basic trigonometric identities (2 marks). Part (ii) applies this result to a double angle equation requiring awareness of the periodic nature within the given domain, but the method is direct once the substitution is made (4 marks total). This is easier than average as it involves routine manipulation of standard trigonometric identities with no conceptual challenges.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals

  1. Given that $$5 \cos \theta - 2 \sin \theta = 0,$$ show that \(\tan \theta = 2.5\) [2]
  2. Solve, for \(0 \leq x \leq 180\), the equation $$5 \cos 2x° - 2 \sin 2x° = 0,$$ giving your answers to 1 decimal place. [4]

\begin{enumerate}[label=(\roman*)]
\item Given that
$$5 \cos \theta - 2 \sin \theta = 0,$$
show that $\tan \theta = 2.5$ [2]

\item Solve, for $0 \leq x \leq 180$, the equation
$$5 \cos 2x° - 2 \sin 2x° = 0,$$
giving your answers to 1 decimal place. [4]
\end{enumerate}

\hfill \mbox{\textit{OCR C2  Q3 [6]}}