Final answer:
The parametric equations for the curve generated by a circle are x = h + r * cos(t) and y = k + r * sin(t). For a circle centered at (0, 0) with a radius of 4, the parametric equations are x = 4 * cos(t) and y = 4 * sin(t).
Step-by-step explanation:
The parametric equations for the curve generated by a circle centered at (h, k) with a radius of r are:
- x = h + r * cos(t)
- y = k + r * sin(t)
For the given circle centered at (0, 0) with a radius of 4, the parametric equations are:
- x = 4 * cos(t)
- y = 4 * sin(t)
These equations describe how the x-coordinate and y-coordinate of a point on the circle change as the parameter t varies. The interval for the parameter values can be any range of values that covers a complete revolution around the circle, such as 0 ≤ t ≤ 2π or -π ≤ t ≤ π.