15 6 points Find an equivalent rectangular equation for the

15) (6 points) Find an equivalent rectangular equation for the curve defined as x 4sint, y= 2 cost, for t in [O,2].

Solution

x = 4sint => sint = x/4

y = 2cost => cost = y/2

=> sin²t + cos²t = (x/4)² + (y/2)²

=> 1 = x²/16 + y²/4

=> 16 = x² + 4y²