| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | December |
| Marks | 6 |
| Topic | Reciprocal Trig & Identities |
| Type | Given one function find others |
| Difficulty | Moderate -0.3 Part (a) is a straightforward application of the Pythagorean identity sin²α + cos²α = 1, requiring simple substitution and square root extraction. Part (b) requires recognizing that tan²β = sec²β - 1 to convert to a quadratic in sec β, then solving—this is slightly more involved but still a standard textbook exercise testing basic trig identities. Overall slightly easier than average due to routine application of well-known identities. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^2 |
3 In this question you must show detailed reasoning.
\begin{enumerate}[label=(\alph*)]
\item Given that $\sin \alpha = \frac { 2 } { 3 }$, find the exact values of $\cos \alpha$.
\item Given that $2 \tan ^ { 2 } \beta - 7 \sec \beta + 5 = 0$, find the exact value of $\sec \beta$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2018 Q3 [6]}}