June 2022 Paper 1 Q1

1 A curve is defined by the parametric equations

\[x = \cos\theta \quad \text{and} \quad y = \sin\theta \qquad \text{where } 0 \leqslant \theta \leqslant 2\pi\]

Which of the options shown below is a Cartesian equation for this curve?

Circle your answer. [1 mark]

• \(\dfrac{y}{x} = \tan\theta\)
• \(x^2 + y^2 = 1\)
• \(x^2 - y^2 = 1\)
• \(x^2y^2 = 1\)