Question

x=cos t, y=cos 2 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 t and find the rectangular-coordinate equation for the curve x = cos(t), y = cos(2t), substitute x = cos(t) into the equation for y to get y = 2x^2 - 1.

Step-by-step explanation:

To find a rectangular-coordinate equation for the curve, you need to eliminate the parameter t. Given that x = cos(t) and y = cos(2t), we can use the trigonometric identities to express y in terms of x. First, let's substitute x = cos(t) into the equation for y:

y = cos(2t) = cos^2(t) - sin^2(t) = x^2 - (1 - x^2) = 2x^2 - 1

Therefore, the rectangular-coordinate equation for the curve is y = 2x^2 - 1.