# 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 ( _, _).

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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rogreenhoxa8

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 $$\displaystyle{r},\theta={2},\pi{4}$$