Finding Cartesian Equation giving Parametric Equations

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The equations are: $$ x = cos(\pi - t), y = sin(\pi - t), 0 \le t \le \pi$$

I don't really understand what to do. On the last problem I had:

$$ x = cos2t, y = sin2t, 0 \le t \le \pi $$

and I just used the basic unit circle of $ x^2 + y^2 = 1 $ but I'm not sure how it was really implemented.

Any help would be appreciated.

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One way to solve your problem is to consider $\pi-t=u$. (This will make it easier to solve.) Now we have:$$x=\cos(u),y=\sin(u)$$Then, we could square both sides to get:$$x^2=\cos^2(u),y^2=\sin^2(u)$$Add the two equations to get:$$x^2+y^2=\cos^2(u)+\sin^2(u)=1$$The last part was the commonly known trigonometric identity derived from the Pythagorean theorem. So the solution is $$x^2+y^2=1$$