Answer
[tex]\left(\sqrt{10},288.4°\right),\left(-\sqrt{10},108.4°\right)[/tex]
Explanation
The polar coordinates can be represented as (r, θ).
Where;
r = √(x² + y²) and θ = tan⁻¹ (y/x)
Hence, the polar coordinates that represent the same point as the rectangular coordinate (1, -3) are calculated below:
[tex]\begin{gathered} x=1,y=-3 \\ r=\sqrt{1^2+(-3)^2}=\sqrt{1+9}=\pm\sqrt{10} \\ \\ \theta=tan^{-1}(-\frac{3}{1})=tan^{-1}(-3)=-71.57 \\ \theta=-71.57+360=288.43^0 \end{gathered}[/tex]
So the answers that apply are:
[tex]\begin{gathered} \left(\pm\sqrt{10},288.4°\right) \\ \Rightarrow\left(\sqrt{10},288.4°\right),\left(-\sqrt{10},(288.4-180)°\right) \\ =\left(\sqrt{10},288.4°\right),\left(-\sqrt{10},108.4°\right) \end{gathered}[/tex]
The second and the last options apply.
