eliminate the parameter. x = 5 cos t, y = 5 sin t. answer must be a rectangular equation

Step-by-step explanation:

Recall the following Pythagorean Identity:

Let's solve the x equation for cos(t) and the y equation for sin(t).

After the solve we will plug into our above identity.

x=5cos(t)

Divide both sides by 5:

(x/5)=cos(t)

y=5sin(t)

Divide both sides by 5:

(y/5)=sin(t)

Now we are ready to plug into the identity:

Multiply both sides by 5^2:

This is a circle with center (0,0) and radius 5.

All I did to get that was compare our rectangular equation we found to

where (h,k) is the center and r is the radius of a circle.