SOLUTION: Convert each point from the given cartesian coordinates to polar coordinates. Find polar coordinates with -pi/2 < theta <= pi/2. a) If (x, y) = (20,-4) then (r, theta)= b) I

Question 828733: Convert each point from the given cartesian coordinates to polar coordinates. Find polar coordinates with -pi/2 < theta <= pi/2.
a) If (x, y) = (20,-4) then (r, theta)=
b) If (x, y) = (1,2) then (r, theta)=
c) If (x, y) = (-2,1) then (r, theta)=
d) If (x, y) = (16,6) then (r, theta)=
e) If (x, y) = (-7,-8) then (r, theta)=
f) If (x, y) = (0,-4) then (r, theta)=
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!

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

 θ = arctan(y/x)  

where
θ = 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) ≈ 20.396

θ = arctan(y/x)
θ = arctan((-4)/(20))
θ = arctan(-0.2)
θ ≈ -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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