# Polar coordinates of point P are given. Find all of its polar coordinates. P=(1,-pi/4)

Polar coordinates of point P are given. Find all of its polar coordinates.
$$\displaystyle{P}={\left({1},-\frac{\pi}{{4}}\right)}$$

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doplovif
A polar coordinate $$\displaystyle{\left({r},θ\right)}$$ can be written in the form:
$$\displaystyle{\left({r},θ+{2}{n}\pi\right)}{\quad\text{or}\quad}{\left(-{r},θ+{\left({2}{n}+{1}\right)}\pi\right)}$$
If $$\displaystyleθ$$ is in radians or:
$$\displaystyle{\left({r},θ+{360}°{n}\right)}{\quad\text{or}\quad}{\left(-{r},θ+{180}°+{360}°{n}\right)}$$
If $$\displaystyleθ$$ is in degrees.
So we write P as:
$$\displaystyle{\left({1},-\frac{\pi}{{4}}+{2}{n}\pi\right)}{\quad\text{and}\quad}{\left(-{1},-\frac{\pi}{{4}}+{\left({2}{n}+{1}\right)}\pi\right)}$$
Where n is an integer.