SOLUTION: Please help me answer the following: (-5,12) are the coordinates of a point in rectangular form. Find this point in polar form (r,A), with A expressed in radians. The answer choi

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Question 150317: Please help me answer the following:
(-5,12) are the coordinates of a point in rectangular form. Find this point in polar form (r,A), with A expressed in radians.
The answer choices include:
1. (13,112.6)
2. (13,1.97)
3. (10.9,1.97)
4. (10.9,112.6)
Thanks, Tami

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me answer the following:
(-5,12) are the coordinates of a point in rectangular form.
Find this point in polar form (r,A), with A expressed in radians.
The answer choices include:
1. (13,112.6)
2. (13,1.97)
3. (10.9,1.97)
4. (10.9,112.6)
Thanks, Tami

Plot the point:



Draw a perpendicular from the point down to the x-axis,
label it y=12, the y-coordinate.

Label the x-coordinate x=-5.

Draw a radius vector (r) from the point to the origin.
Indicate the angle A with a curved line.



Now we calculate r using the Pythagorean theorem:

 

And we calculate angle A by the trig equation

tan%28A%29=y%2Fx

tan%28A%29=-12%2F5

We find the reference angle using the inverse tangent:
Tan%5E%28-1%29%2812%2F5%29=1.1760 

However, since this angle is in the second quadrant, we
find the angle A by subtracting the reference angle from pi

A+=+pi-1.1760+=+3.1416-1.1760+=+1.9656 or about 1.97



Now we place it in the form

(r,A) = (13,1.97), choice 2

Edwin