Polar Coordinates
Given a point in coordinates (r, θ), the equivalent point in cartesian coordinates (x, y) can be found as:
x = r cos θ
y = r sin θ
We are given the point:
[tex](4,\frac{7\pi}{4})[/tex]
Converting to cartesian coordinates:
[tex]\begin{gathered} x=4\cos(\frac{7\pi}{4}) \\ x=4*\frac{\sqrt{2}}{2} \\ x=2\sqrt{2} \end{gathered}[/tex][tex]\begin{gathered} y=4\sin(\frac{7\pi}{4}) \\ y=4*(-\frac{\sqrt{2}}{2}) \\ y=-2\sqrt{2} \end{gathered}[/tex]
The cartesian coordinates are:
[tex](2\sqrt{2},-2\sqrt{2})[/tex]
