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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: 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(2043) 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:

drawing(400,400,-13,13,-13,13, graph(400,400,-13,13,-13,13), locate(-9,12.5,'(-5,12)'), locate(-5-.2,12+.4,o) )

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.

drawing(400,400,-13,13,-13,13, graph(400,400,-13,13,-13,13,sqrt(16-x^2)sqrt(x+1.538)/sqrt(x+1.538)), locate(-7.4,6,'y=12'), locate(-4,1.5,'x=-5'), locate(2,4.2,'A'), locate(-3,9,'r'),
triangle(0,0,-5,12,-5,0),locate(-9,12.5,'(-5,12)'), locate(-5-.2,12+.4,o) )

Now we calculate r using the Pythagorean theorem:

r=sqrt(x^2+y^2)=sqrt((-5)^2+12^2)=sqrt(25+144)=sqrt(169)=13 

And we calculate angle A by the trig equation

tan(A)=y/x

tan(A)=-12/5

We find the reference angle using the inverse tangent:
Tan^(-1)(12/5)=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

drawing(400,400,-13,13,-13,13, graph(400,400,-13,13,-13,13,sqrt(16-x^2)sqrt(x+1.538)/sqrt(x+1.538)), locate(-7.4,6,'y=12'), locate(-4,1.5,'x=-5'), locate(2,4.2,'A=1.97'), locate(-3,9,'r=13'),
triangle(0,0,-5,12,-5,0),locate(-9,12.5,'(-5,12)'), locate(-5-.2,12+.4,o) )

Now we place it in the form

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

Edwin