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

<pre><font size = 4 color = "indigo"><b>
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</pre>