| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trigonometric equations in context |
| Type | Solve shifted trig equation |
| Difficulty | Moderate -0.3 Part (i) is a straightforward phase-shifted cosine equation requiring basic inverse trig and angle adjustment. Part (ii) involves using the Pythagorean identity to convert to a quadratic in sin θ, then solving—standard C2 technique but requires multiple steps. Both are routine textbook exercises with no novel insight needed, making this slightly easier than average. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
8 In this question solutions based entirely on graphical or numerical methods are not acceptable.\\
(i) Solve for $0 \leqslant x < 360 ^ { \circ }$,
$$4 \cos \left( x + 70 ^ { \circ } \right) = 3$$
giving your answers in degrees to one decimal place.\\
(ii) Find, for $0 \leqslant \theta < 2 \pi$, all the solutions of
$$6 \cos ^ { 2 } \theta - 5 = 6 \sin ^ { 2 } \theta + \sin \theta$$
giving your answers in radians to 3 significant figures.\\
\hfill \mbox{\textit{Edexcel C2 2018 Q8 [9]}}