| Exam Board | OCR |
|---|
| Module | C3 (Core Mathematics 3) |
|---|
| Year | 2014 |
|---|
| Session | June |
|---|
| Topic | Harmonic Form |
|---|
9
- Express \(5 \cos \left( \theta - 60 ^ { \circ } \right) + 3 \cos \theta\) in the form \(R \sin ( \theta + \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\).
- Hence
(a) give details of the transformations needed to transform the curve \(y = 5 \cos \left( \theta - 60 ^ { \circ } \right) + 3 \cos \theta\) to the curve \(y = \sin \theta\),
(b) find the smallest positive value of \(\beta\) satisfying the equation
$$5 \cos \left( \frac { 1 } { 3 } \beta - 40 ^ { \circ } \right) + 3 \cos \left( \frac { 1 } { 3 } \beta + 20 ^ { \circ } \right) = 3 .$$
\section*{END OF QUESTION PAPER}