Answer
(a) Polar coordinates are defined as $(r,θ)$
where $r$ is the length between point $(0,0)$ to the point $(x,y)$ and $θ$ is the angle between $r$ and the $x$ axis.
(b) Cartesian coordinates $(x,y)$ of a point in terms of the polar coordinates can be deifned by equations such as
$$x=r cos(θ), y=rsin(θ)$$
(c) To find the polar coordinates $(r,θ)$ of a point, we have to first need to calculate the length of the radius $r$, in order to find this we will use the equation $$r=\sqrt (x^{2}+y^{2})$$,
Then we need to find the angle between the radius and the x axis, in order to find this we will take the help of the equations $$θ=tan^{-1}\frac{y}{x}$$.
Work Step by Step
(a) Polar coordinates are defined as $(r,θ)$
where $r$ is the length between point $(0,0)$ to the point $(x,y)$ and $θ$ is the angle between $r$ and the $x$ axis.
(b) Cartesian coordinates $(x,y)$ of a point in terms of the polar coordinates can be deifned by equations such as
$$x=r cos(θ), y=rsin(θ)$$
(c) To find the polar coordinates $(r,θ)$ of a point, we have to first need to calculate the length of the radius $r$, in order to find this we will use the equation $$r=\sqrt (x^{2}+y^{2})$$,
Then we need to find the angle between the radius and the x axis, in order to find this we will take the help of the equations $$θ=tan^{-1}\frac{y}{x}$$.