Question

Curves Represented

Hint:

For parametric equations, remember that \( t \) serves as a parameter that helps trace out curves in the plane. You can plot the curves by substituting different values of \( t \).

Answer 1

These are parametric equations that represent a set of curves in the coordinate plane. The variable \( t \) is a parameter that dictates the values of both \( x \) and \( y \). By adjusting \( t \), the curves can be traced out.
- The equation \( x = 3 (\cos t + \sin t) \) represents the \( x \)-coordinate in terms of \( t \).
- The equation \( y = (\cos t - \sin t) \) represents the \( y \)-coordinate in terms of \( t \).