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# Polar Coordinates

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How do I find the polar coordinates of (-52, 75)?? I think I'm doing it right but my answers come out wrong every time

May 11, 2017

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Remember that θ is the angle that a line from the origin to the point makes with the positive x axis. That is, the line to the right of the y-axis.

To find r, we can use the Pythagorean theorem.

(-52)2 + 752 = r2

$$\sqrt{2704+5625}$$ = r

$$\sqrt{8329}$$ = r

r ≈ 91.26

To find θ, we can take the arctan(75/-52) ...

arctan(75/-52) ≈ -55.27º

But..the calculator gives us an angle that lies in the fourth quadrant.

The tangent values repeat every 180º ...so just add 180º to get the angle that has the same tangent in the second quadrant.

-55.27º + 180º = 124.73º ≈ θ

So...the polar coordinates are (91.26, 124.73º)

May 11, 2017