SchachtN

2021-09-29

For the polar point $\left(-4,-\frac{3\pi }{4}\right)$
a) Give alternate coordinates with $r>0$ and $-2\pi \le \theta <0$.
b) Give alternate coordinates with $r<0$ and $0\le \theta <2\pi$.
c) Give alternate coordinates of your choice.

Willie

Step 1
Given: $P\left(-4,-\frac{3\pi }{4}\right)$
a) $\left(-4,-\frac{3\pi }{4}\right)=\left(4,-\frac{3\pi }{4}+\pi \right)$
$=\left(4,\frac{\pi }{4}\right)$
So, $\left(-4,-\frac{3\pi }{4}\right)=\left(4,\frac{\pi }{4}\right)$
Step 2
b) $\left(-4,-\frac{3\pi }{4}\right)=\left(-4,-\frac{3\pi }{4}+2\pi \right)$
$=\left(-4,-\frac{5\pi }{4}\right)$
So, $\left(-4,-\frac{3\pi }{4}\right)=\left(-4,\frac{5\pi }{4}\right)$
c) $\left(-4,-\frac{3\pi }{4}\right)=\left(4,-\frac{3\pi }{4}+3\pi \right)$
$=\left(4,\frac{9\pi }{4}\right)$
So, $\left(-4,-\frac{3\pi }{4}\right)=\left(4,\frac{9\pi }{4}\right)$

Jeffrey Jordon

Answer is given below (on video)

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