find cartesian equation and domain and range of this

Question

For the pair of parametric equations below, eliminate the parameter to find its Cartesian equation. Also specify the domain and range of your equation using interval notation.

Answer 1

To get cartesian equation we square given equations and then add: x²(t) = 4cos²(t), y²(t) = 4sin²(t).

So, x² + y² = 4(cos²(t) + sin²(t)), or x² + y² = 4. We have circle with center at origin and radius 2.

Domain: - 2 ≤ x ≤ 2;

Range: - 2 ≤ y ≤ 2;