Question

Find a rectangular equation of the curve whose parametric equations are x=2cos(t) and y=2sin(t) where 0 is less than or equal to t which is less than or equal to 2pi. Then graph the equation using arrows to indicate how the graph is traced.

Answer 1

\[x=2\cos t\]
\[y=2\sin t\]
where 0 ≤ t ≤ 2π
\[x^2 + y^2 = (2 \cos t)^2 + (2 \sin t)^2 = 4 \cos^2t + 4 \sin^2t = 4(\cos^2t + \sin^2t) = 4\]
\[x^2 + y^2 = 4\]
Circle, center at origin, radius 2