Question

Given the parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π. convert to a rectangular equation and sketch the curve

Answer 1

The rectangular equation for given parametric equations x = 2sin(t) and   y = -3cos(t) on 0 ≤ t ≤ π is  $\frac{x^{2} }{4} +\frac{y^2}{9} =1$ which is an ellipse.

For given question,

We have been given a pair of parametric equations x = 2sin(t) and           y = -3cos(t) on 0 ≤ t ≤ π.

We need to convert given parametric equations to a rectangular equation and sketch the curve.

Given parametric equations can be written as,

x/2 = sin(t) and y/(-3) = cos(t) on 0 ≤ t ≤ π.

We know that the trigonometric identity,

sin²t + cos²t = 1

⇒ (x/2)² + (- y/3)² = 1

⇒ $\frac{x^{2} }{4} +\frac{y^2}{9} =1$

This represents an ellipse with center (0, 0), major axis 18 units and minor axis 8 units.

The rectangular equation is  $\frac{x^{2} }{4} +\frac{y^2}{9} =1$

The graph of the rectangular equation $\frac{x^{2} }{4} +\frac{y^2}{9} =1$ is as shown below.

Therefore, the rectangular equation for given parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π is  $\frac{x^{2} }{4} +\frac{y^2}{9} =1$ which is an ellipse.

Learn more about the parametric equations here:

brainly.com/question/14289251

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