Question 828733
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Hi, there--

THE PROBLEM:
a) If (x, y) = (20,-4) then (r, theta)= 

A SOLUTION:
We use these conversions to translate from Cartesian to Polar Coordinates. Note the quadrant 
in which (x,y) lies in order to select the correct angle (between -pi/2 and pi/2).

r = sqrt(x^2 + y^2)

where
r is distance from origin to the point
x is value of the x-coordinate
y is value of the y-coordinate

 &#952; = arctan(y/x)  

where
&#952; = angle relative to the zero axis (in degrees)


Given (x, y) = (20,-4) then

r = sqrt(x^2 + y^2)
r = sqrt((20)^2 + (-4)^2) 
r = sqrt(400 + 16) 
r = sqrt(416) 
r = 2*sqrt(104) &#8776; 20.396

&#952; = arctan(y/x)
&#952; = arctan((-4)/(20))
&#952; = arctan(-0.2)
&#952; &#8776; -0.197

The polar coordinates (in radians) are approximately (20.396, -0.197).

Try the rest on your own. 


Hope this helps! Feel free to email if you have any questions or want to check your answers.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com
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