| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2013 |
| Session | November |
| Topic | Harmonic Form |
| Type | Find value where max/min occurs |
| Difficulty | Moderate -0.3 This is a standard harmonic form question requiring routine application of the R sin(x - α) formula using R = √(1² + (√8)²) = 3 and tan α = √8/1, then reading off the maximum value R = 3 at x = α + 90°. While it involves multiple steps, the technique is formulaic and commonly practiced, making it slightly easier than average. |
| Spec | 1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc1.05o Trigonometric equations: solve in given intervals |
8 (i) Express $\sin x - \sqrt { 8 } \cos x$ in the form $R \sin ( x - \alpha )$ where $R \geqslant 0$ and $0 \leqslant \alpha \leqslant 90 ^ { \circ }$.\\
(ii) Hence write down the maximum value of $\sin x - \sqrt { 8 } \cos x$ and find the smallest positive value of $x$ for which it occurs.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2013 Q8}}