Applications of Parametric Equations 4

Question

Eliminate the parameter.  x = 3 cos t, y = 3 sin t

Answer 1

 x = 3 cos t ⇒ cos(t) = x/3.

y = 3 sin t ⇒ sin(t) = y/3.

Pythagorean identity : sin² θ + cos² θ = 1.

sin²(t) + cos²(t) = 1

(y/3)² + (x/3)² = 1

y²/9 + x²/9 = 1

x² + y² = 9.

The rectangular equation is x² + y² = 9.