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

Falak Kinney 2021-09-12 Answered

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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Expert Answer

doplovif
Answered 2021-09-13 Author has 18799 answers
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.
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