We can describe the location of a point in the plane using different ________ systems. The point P shown in the figure has rectangular coordinates ( _ , _ ) and polar coordinates ( _, _).

Rivka Thorpe 2021-08-05 Answered
We can describe the location of a point in the plane using different ________ systems. The point P shown in the figure has rectangular coordinates ( _ , _ ) and polar coordinates ( _, _).
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Expert Answer

rogreenhoxa8
Answered 2021-08-06 Author has 16060 answers

Step 1
Given,
point p on graph
from coordinates system point is on (1,1)
\(\displaystyle{x}={1}\) and \(\displaystyle{y}={1}\) on point P
we know polar coordinates is \(\displaystyle{r},\theta\) where
\(\displaystyle{x}={r}{\cos{\theta}}{y}={r}{\sin{\theta}}\)
\(\displaystyle{x}{2}+{y}{2}={r}{2}{\cos{{2}}}\theta+{r}{2}{\sin{{2}}}\theta{x}{2}+{y}{2}={r}{2}{\sin{{2}}}\theta+{\cos{{2}}}\theta{r}={x}{2}+{y}{2}\)
now put values of x and y
Step 2
\(\displaystyle{r}={1}+{1}={2}\)
divide equation 1 from 2
\(\displaystyle{r}{\sin{\theta}}{r}{\cos{\theta}}={y}{x}{\tan{\theta}}={1}\)
\(\displaystyle\theta=\pi{4}\)
so, coordinate points is \(\displaystyle{x},{y}={1},{1}\)
polar coordinate \(\displaystyle{r},\theta={2},\pi{4}\)

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