Solution:
Given:
[tex]\begin{gathered} (4,\frac{7\pi}{4}) \\ where; \\ r=4 \\ \theta=\frac{7\pi}{4} \end{gathered}[/tex]
To convert from polar to cartesian coordinates,
[tex]\begin{gathered} x=rcos\theta \\ y=rsin\theta \end{gathered}[/tex][tex]\begin{gathered} x=4cos\frac{7\pi}{4} \\ x=\frac{4\sqrt{2}}{2} \\ x=2\sqrt{2} \end{gathered}[/tex][tex]\begin{gathered} y=4sin\frac{7\pi}{4} \\ y=4(\frac{-\sqrt{2}}{2}) \\ y=-2\sqrt{2} \end{gathered}[/tex]
Hence, the pair as a cartesian coordinate as an ordered pair is;
[tex](2\sqrt{2},-2\sqrt{2})[/tex]
