| Exam Board | CAIE |
|---|
| Module | P2 (Pure Mathematics 2) |
|---|
| Year | 2005 |
|---|
| Session | June |
|---|
| Topic | Parametric equations |
|---|
5
- By differentiating \(\frac { 1 } { \cos \theta }\), show that if \(y = \sec \theta\) then \(\frac { \mathrm { d } y } { \mathrm {~d} \theta } = \sec \theta \tan \theta\).
- The parametric equations of a curve are
$$x = 1 + \tan \theta , \quad y = \sec \theta$$
for \(- \frac { 1 } { 2 } \pi < \theta < \frac { 1 } { 2 } \pi\). Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \sin \theta\).
- Find the coordinates of the point on the curve at which the gradient of the curve is \(\frac { 1 } { 2 }\).