Answer
$x^{2}+y^{2}=1,\quad y\geq 0$
Work Step by Step
Square both parametric equations:
$x^{2}=\cos^{2}(\pi-t)$
$y^{2}=\sin^{2}(\pi-t)$
Add the two equations:
$x^{2}+y^{2}=1$
To graph, create a function value table using values for t, in ascending order of t, calculating the x- and y-coordinates of points on the graph.
Plot and join the points obtained with a smooth curve, noting the direction in which t increases.
Note that when t ranges from $0$ to $\pi,$ only the upper semicircle is traced.
So, we restrict the Cartesian equation:
$x^{2}+y^{2}=1,\quad y\geq 0$
