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.

Start practising Read the lesson

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.
Level 2 · 2 marksTry it
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
4
The diagram shows a curve $C$ with parametric equations $x = 5\cos t,\ y = 2\sin t$ , $0 \le t < 2\pi$ .Find a Cartesian equation of $C$ .
Level 3 · 2 marksTry it
5
A curve has parametric equations $x = 2 + 3\cos t,\ y = 1 + 3\sin t$ . Find a Cartesian equation of the curve and state its centre and radius.
Level 3 · 2 marksTry it

11 more questions on parametric curves and trig identities

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free