parametric equation

Question

Graph the pair of the parametric equation

 

x = 6 sin t
y = 6 cos t, 0 ≤ t ≤ 2π 

Answer 1

x = 6 sin t ⇒ sin(t) = x/6.

y = 6 cos t ⇒ cos(t) = y/6, 0 ≤ t ≤ 2π.

Pythagorean identity : sin² θ + cos² θ = 1.

sin²(t) + cos²(t) = 1

(x/6)² + (y/6)² = 1

x²/36 + y²/36 = 1

x² + y² = 36.

The above equation represent the circle x² + y² = r².

Center at (0, 0) and r = 6,So we plot

Up (0, 0+6) = (0, 6)

Down (0, 0-6) = (0, -6)

Left (0-6, 0) = (-6, 0)

Right (0+6, 0) = (0, 6)

Graph

1. draw the coordinate plane.

2. Plot the center at (-5,9).

3. Plot 4 points " radius away from the center in the up, down, left and right direction.

4. Sketch the circle.