| Exam Board | AQA |
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| Module | C4 (Core Mathematics 4) |
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| Year | 2011 |
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| Session | June |
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| Topic | Parametric equations |
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4
- A curve is defined by the parametric equations \(x = 3 \cos 2 \theta , y = 2 \cos \theta\).
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { k \cos \theta }\), where \(k\) is an integer.
- Find an equation of the normal to the curve at the point where \(\theta = \frac { \pi } { 3 }\).
- Find the exact value of \(\int _ { - \frac { \pi } { 4 } } ^ { \frac { \pi } { 4 } } \sin ^ { 2 } x \mathrm {~d} x\).