| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Quadratic trigonometric equations |
| Type | Show then solve: tan/sin/cos identity manipulation |
| Difficulty | Moderate -0.3 This is a standard C2 trigonometric equation requiring conversion to quadratic form using tan x = sin x/cos x and the Pythagorean identity. Part (i) is guided algebraic manipulation, and part (ii) is routine quadratic solving followed by finding angles. Slightly easier than average due to the scaffolding provided in part (i). |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}
\item (i) Given that
\end{enumerate}
$$8 \tan x - 3 \cos x = 0$$
show that
$$3 \sin ^ { 2 } x + 8 \sin x - 3 = 0$$
(ii) Find, to 2 decimal places, the values of $x$ in the interval $0 \leq x \leq 2 \pi$ such that
$$8 \tan x - 3 \cos x = 0$$
\hfill \mbox{\textit{OCR C2 Q5 [8]}}