| Exam Board | Edexcel |
|---|---|
| Module | C34 (Core Mathematics 3 & 4) |
| Year | 2018 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Harmonic Form |
| Type | Range of simple harmonic function |
| Difficulty | Standard +0.3 This is a standard harmonic form question with routine techniques: (a) uses the R cos(θ+α) formula with straightforward calculation, (b) applies the result to solve a trigonometric equation in a given range, and (c) uses range properties (max/min = B ± AR) requiring simple simultaneous equations. All parts follow textbook methods with no novel insight required, making it slightly easier than average. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc1.05o Trigonometric equations: solve in given intervals |
6. (a) Express $\sqrt { 5 } \cos \theta - 2 \sin \theta$ in the form $R \cos ( \theta + \alpha )$, where $R > 0$ and $0 < \alpha < \frac { \pi } { 2 }$
State the value of $R$ and give the value of $\alpha$ to 4 significant figures.\\
(b) Solve, for $- \pi < \theta < \pi$,
$$\sqrt { 5 } \cos \theta - 2 \sin \theta = 0.5$$
giving your answers to 3 significant figures. [Solutions based entirely on graphical or numerical methods are not acceptable.]
$$\mathrm { f } ( x ) = A ( \sqrt { 5 } \cos \theta - 2 \sin \theta ) + B \quad \theta \in \mathbb { R }$$
where $A$ and $B$ are constants.
Given that the range of f is
$$- 15 \leqslant f ( x ) \leqslant 33$$
(c) find the value of $B$ and the possible values of $A$.
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\hfill \mbox{\textit{Edexcel C34 2018 Q6 [11]}}