Question

a point in the xy plane has Cartesian coordinates (-3.0,5) m What are the polar coordinates of the point?

Answer 1

Take into account that transformation from cartesian coordinates to polar coordiantes can be written as follow:

P(x,y) => P(r,θ)

To find the value if r, use:

`r=\sqrt[]{x^2+y^2}=\sqrt[]{(-3)^2+(5)^2}=\sqrt[]{9+25}=\sqrt[]{34}`

To find the value of θ, use:

`\theta=\tan ^(-1)((y)/(x))=\tan ^(-1)((5)/(-3))\approx-59.0`

Then, the polar coordinates of the points are:

r = √34

θ = -59.0