CAIE P1 2015 June — Question 1 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2015
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTrig Graphs & Exact Values
TypeFind exact trig values from given ratio
DifficultyEasy -1.2 This is a straightforward application of basic trigonometric identities requiring minimal problem-solving. Part (i) uses Pythagorean identity with sign consideration for obtuse angles, (ii) is immediate division, and (iii) applies a standard angle addition formula. All are routine recall-based exercises with clear single-step solutions.
Spec1.05a Sine, cosine, tangent: definitions for all arguments1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae

Given that \(\theta\) is an obtuse angle measured in radians and that \(\sin \theta = k\), find, in terms of \(k\), an expression for
  1. \(\cos \theta\), [1]
  2. \(\tan \theta\), [2]
  3. \(\sin(\theta + \pi)\). [1]

Given that $\theta$ is an obtuse angle measured in radians and that $\sin \theta = k$, find, in terms of $k$, an expression for

\begin{enumerate}[label=(\roman*)]
\item $\cos \theta$, [1]
\item $\tan \theta$, [2]
\item $\sin(\theta + \pi)$. [1]
\end{enumerate}

\hfill \mbox{\textit{CAIE P1 2015 Q1 [4]}}