Question

x=2 sin(t) , y=2cos(t), 0 ≤ t ≤ π A pair of parametric equations is given. Sketch the curve represented by the parametric equations.

Answer 1

The curve represented by the given parametric equations is a circle with radius 2, centered at the origin (0, 0).

Step-by-step explanation:

To sketch the curve represented by the given parametric equations, we can eliminate the parameter t and plot the resulting equation in the xy-plane. Using the trigonometric identity sin^2(t) + cos^2(t) = 1, we can square both equations and add them together:

x^2 + y^2 = (2 sin(t))^2 + (2 cos(t))^2 = 4 (sin^2(t) + cos^2(t)) = 4

Thus, the curve represented by the parametric equations is a circle with radius 2, centered at the origin (0, 0). The range of t from 0 to π corresponds to an arc of the circle.