Answer
a)
Polar coordinates are written in the form: $(r,θ)$.
b)
$x=r cos(θ), y=rsin(θ)$.
c)
$r=\sqrt (x^{2}+y^{2})$, $θ=tan^{-1}\frac{y}{x}$.
Work Step by Step
a)
Polar coordinates are written in the form $(r,θ)$, where $r$ is the length between point $(0,0)$ and point $(x,y)$, and $θ$ is the angle between $r$ and the x-axis.
b)
The equations that express the Cartesian coordinates $(x,y)$ of a point in terms of the polar coordinates are: $x=r cos(θ), y=rsin(θ)$.
c)
To find the polar coordinates $(r,θ)$ of a point, we first need to calculate the length of the radius. We can do this by using the equation $r=\sqrt (x^{2}+y^{2})$. Then we need to find the angle between the radius and the x axis. We can do this by using the equation $θ=tan^{-1}\frac{y}{x}$.
