I need help with polar coordinates!?

Question

1. Find the polar coordinates of (32, -60) for r > 0.

[A] (-68, 298.1°)
[B] (68, 151.9°)
[C] (68, 241.9°)
[D] None of these


2. Find the polar coordinates of (-4, -4) for r > 0
[A] (8√2, 135°)
[B] (4√2, 315°)
[C] (4√2, 225°)
[D] None of these

3. Find the polar coordinates of (-12, -12) for r > 0
[A] (8, 135°)
[B] (12√2, 135°)
[C] (12√2, 315°)
[D] None of these


Thank you!

Answer 1

r=sqrt(x^2+y^2) and theta = tan^-1(y/x)

r = sqrt(32^2+60^2) = 68
theta = tan-1(-60/32) = 298.1
answer is D

r = sqrt(4^4+4^4) = 4sqrt(2)
theta = tan^-1(-4/-4) = 45 this is i quad 3, so = 225
ans is C

r = 12sqrt(2)
theta is 225 again

ans i D

Answer 2

1). r^2 = x^2 + y^2
r^2= 32^2+(-60)^2
r= 68

For the angle,
x positive and y negative means that the point is in the 4th Quadrant, therefore:
alpha = arctan (-60/32)
= -61.9 degree
= -61.9 + 360
= 298.1 degree
(Note that you can add or substract 360 from your answer as many time as you want to make your answer fit in the interval)
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2). Use the same method to find r.
r^2=x^2+y^2
r^2=(-4)^2+(-4)^2
r=4(2)^(1/2) or 4 times root 2

For the angle,
x negative and y negative means that the point is in 3rd Quadrant.
alpha = arctan (-4/-4)
= 45 degrees

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3). Using the same method as number 2)
r ^2= x^2 + y^2
we get r = 12root(2) or 12x2^(1/2)

and alpha equal 225 degrees