How do you convert the Cartesian coordinates (1.1 m, 1.6 m) to polar coordinates?

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How do you convert the Cartesian coordinates (1.1 m, 1.6 m) to polar coordinates?

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Answer 1 · 2016-02-14T02:42:41

Rectangular (Cartesian) coordinates are in the form $(x, y)$ $(x,y)$ , polar coordinates in the form $(r, θ)$ $(r,theta)$ . In this case the polar coordinates are $(1.45, 0.97)$ $(1.45,0.97)$ .

Explanation:

First step is to find $r$ $r$ , the distance of the point from the origin:

$r = \sqrt{x^{2} + y^{2}} = \sqrt{{1.1}^{2} + {1.6}^{2}} = \sqrt{3.77} = 1.94$ $r=sqrt(x^2+y^2)=sqrt(1.1^2+1.6^2)=sqrt3.77=1.94$ $m$ $m$ .

Now we need to find the angle, $θ$ $theta$ , in radians, counterclockwise from the positive $x$ $x$ axis. To do this we use trigonometry: the $x$ $x$ and $y$ $y$ coordinates are the adjacent and opposite sides respectively of a right-angled triangle.

$tan θ = \frac{o p p}{a d j} = \frac{1.6}{1.1} = 1.45$ $tan theta=(opp)/(adj)=1.6/1.1=1.45$

$θ = {tan}^{- 1} (1.45) = 0.97$ $theta=tan^-1(1.45)=0.97$ radians

Putting it together, the polar coordinates of the point are $(1.45, 0.97)$ $(1.45,0.97)$ .

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How do you convert the Cartesian coordinates (1.1 m, 1.6 m) to polar coordinates?

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