Question

Eliminate the parameter.

x = 5 cos t, y = 5 sin t

Answer 1

@Chooch146 @some_someone

Answer 2

@FLVS-Math

Answer 3

$$
\text{one can say that}\\
x=5cos(t) \implies cos(t)=\cfrac{x}{5}\\
\text{and that}\\
y=5sin(t) \implies sin(t)=\cfrac{y}{5}\\
\text{now, using the pythagorean identity}\\
\color{blue}{sin^2(t)+cos^2(t)=1}\\
$$

one can say that ?
can you take it from there?

Answer 4

how do i get rid of the (t) tho? @jdoe0001

Answer 5

@Mertsj @timo86m

Answer 6

@Chooch146

Answer 7

\[x=5\cos t\\
y=5\sin t\]
Like @jdoe0001 said, you have to make use of the Pythagorean identity, \(\sin^2\theta+\cos^2\theta=1\).
If you plug in the given expressions for \(x\) and \(y\), you have something like
\[(5\sin t)^2+(5\cos t)^2=1\\
25\sin^2t+25\cos^2t=1\\
25\left(\sin^2t+\cos^2t\right)=1\\
25=1\]
However, this isn't true, so you have to adjust a bit. Multiply the right side by 25 to make it true:
\[(5\sin t)^2+(5\cos t)^2=25\]
Finally, to eliminate the parameter \(t\), substitute the parametric equations:
\[x^2+y^2=25\]