| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Equation with 'show that' rewriting preliminary part |
| Difficulty | Moderate -0.3 This is a standard C3 trigonometric equation question with routine steps: (a) is basic calculator work, (b) uses the standard identity sec²x = 1 + tan²x requiring simple algebraic manipulation, and (c) applies the quadratic formula to solve for tan x then finds angles. All techniques are textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals |
3
\begin{enumerate}[label=(\alph*)]
\item Solve the equation $\tan x = - \frac { 1 } { 3 }$, giving all the values of $x$ in the interval $0 < x < 2 \pi$ in radians to two decimal places.
\item Show that the equation
$$3 \sec ^ { 2 } x = 5 ( \tan x + 1 )$$
can be written in the form $3 \tan ^ { 2 } x - 5 \tan x - 2 = 0$.
\item Hence, or otherwise, solve the equation
$$3 \sec ^ { 2 } x = 5 ( \tan x + 1 )$$
giving all the values of $x$ in the interval $0 < x < 2 \pi$ in radians to two decimal places.\\
(4 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2009 Q3 [8]}}