Question

x= sin² t, y=cos t A pair of parametric equations is given. Find a rectangular-coordinate equation for the curve by eliminating the parameter.

Answer 1

To eliminate the parameter and convert the parametric equations x = sin²t and y = cos t to a rectangular-coordinate equation, we need to express x in terms of y. The rectangular-coordinate equation is √x = y.

Step-by-step explanation:

To eliminate the parameter and convert the parametric equations x = sin²t and y = cost to a rectangular-coordinate equation, we need to express x in terms of y. From the equation x = sin²t, we know that sin²t = x. Taking the square root of both sides, we get sin t = √x. Since y = cos t, we can substitute cos t for y. So, the rectangular-coordinate equation becomes:

√x = y