A-level · Coordinate geometry

Parametric curves and trig identitiesExam-style questions

Converting trigonometric parametric equations to Cartesian form using identities — sin²+cos²≡1 for circles and ellipses, sec²−tan²≡1, and the double-angle formulae — and recognising the curve that results.

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16 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
A curve has parametric equations $x = 3\cos t,\ y = 2\sin t$ .
(a) Find a Cartesian equation of the curve.
(b) State the range of values of $x$ and of $y$ .
Level 4 · 4 marksTry it
2
A curve has parametric equations $x = \sec t,\ y = \tan t$ . Show that a Cartesian equation of the curve is $x^2 - y^2 = 1$ .
Level 4 · 2 marksTry it
3
A curve has parametric equations $x = 2\sin t,\ y = \cos 2t$ . Find a Cartesian equation of the curve in the form $y = f(x)$ , and state the range of values of $x$ .
Level 4 · 3 marksTry it
4
A curve has parametric equations $x = 3\sin t, \; y = \cos 2t$ .

Find a Cartesian equation of the curve. (4 marks)
Level 4 · 4 marksTry it
5
A curve has parametric equations $x = 2\tan t, \; y = \sec^{2} t$ .

Find a Cartesian equation of the curve. (4 marks)
Level 4 · 4 marksTry it

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