| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trigonometric equations in context |
| Type | Solve shifted trig equation |
| Difficulty | Moderate -0.3 Part (a) is a straightforward phase-shifted sine equation requiring basic inverse trig and angle adjustment. Part (b) involves a standard quadratic substitution using the Pythagorean identity (sin²x = 1 - cos²x), then solving a quadratic in cos x. Both are routine C2-level techniques with no novel problem-solving required, making this slightly easier than average but not trivial due to the multi-step nature and need for careful angle work. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}
\item In this question you must show all stages of your working. (Solutions based entirely on graphical or numerical methods are not acceptable.)\\
(a) Solve for $0 \leqslant x < 360 ^ { \circ }$, giving your answers in degrees to 1 decimal place,
\end{enumerate}
$$3 \sin \left( x + 45 ^ { \circ } \right) = 2$$
(b) Find, for $0 \leqslant x < 2 \pi$, all the solutions of
$$2 \sin ^ { 2 } x + 2 = 7 \cos x$$
giving your answers in radians.\\
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\hfill \mbox{\textit{Edexcel C12 Q14 [10]}}