Question

Please help! (-2,-2sqrt3) from rectangular coordinates to polar coordinates? a. (4, 120°)
b. (4, 150°) c. (4, 210°) d. (4, 240°)

Answer 1

So the x and y coordinates, how might you translate that into a single line from the center? You can use the pythagorean theorem since the distance to that point from the origin is just a hypotenuse of a triangle with a height of y and length of x.

Now how do you find the angle? Well what function gives you an angle? Inverse trig functions. What information do you have to find that? The x and y, which is the same as the opposite and adjacent sides ins SOH CAH TOA, so we can see we'll be using inverse tangent to find the angle!

Answer 2

Oh o.k. Makes sense! Can you please go through solving step by step with me though? I'm having lots of trouble :/

Answer 3

Sure, show me your work and try it out and I'll help you along.

Answer 4

Is it b.?

Answer 5

So basically when you look at the point on a graph, it looks like this: and it's 4 away and 60 degrees below the x-axis, however...

Answer 6

Like Kainui said, think of this as a triangle.
The A here correlates to your x length from the origin (-2), B correlates to your y distance from the origin (-2√3).
What I would do first is find out your C value using the Pythagorean theorem:
A^2 + B^2 = C^2
(-2)^2 + (-2√3)^2 = C^2
4 + 12 = C^2
16 = C^2
4 = C
Then find out what your theta value is by using trigonometric identities.

Opposite/adjacent is the role of tangent, so we have:
tan(θ) = B/A
tan(θ) = (2√3)/2
θ = tan^-1[(2√3)/2]
θ = π/3
Since we know that one π is equivalent to 180°, we can easily reason that π/3 is equivalent to 60° meaning your total angle is 240°, and your distance out is 4.
In polar form, (-2, -2√3) correlates to (4, 240°).