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 $x = \cos t,\ y = \sin t$ , $0 \le t < 2\pi$ . Find a Cartesian equation of the curve and describe it.
Level 2 · 2 marksTry it
2
A curve has parametric equations $x = 4\cos t,\ y = 4\sin t$ . Find a Cartesian equation of the curve and state its centre and radius.
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3
A curve has parametric equations $x = 5\sin t, \; y = 5\cos t$ , $\; 0 \leqslant t < 2\pi$ .

Find a Cartesian equation of the curve. (2 marks)
Level 2 · 2 marksTry it