| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Find exact trig values from given ratio |
| Difficulty | Easy -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. |
| Spec | 1.05a 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
\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]}}