Question

If answer one is (sqrt10, 288.4°), what is the second answer to this problem?

Answer 1

`\left(√(10),288.4°\right),\left(-√(10),108.4°\right)`

Step-by-step 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:

`\begin{gathered} x=1,y=-3 \\ r=√(1^2+(-3)^2)=√(1+9)=\pm√(10) \\ \\ \theta=tan^(-1)(-(3)/(1))=tan^(-1)(-3)=-71.57 \\ \theta=-71.57+360=288.43^0 \end{gathered}`

So the answers that apply are:

`\begin{gathered} \left(\pm√(10),288.4°\right) \\ \Rightarrow\left(√(10),288.4°\right),\left(-√(10),(288.4-180)°\right) \\ =\left(√(10),288.4°\right),\left(-√(10),108.4°\right) \end{gathered}`

The second and the last options apply.