3. The rectangular coordinates of a point are given. Find the polar coordinates of each point.
b. (0,3)
I figured out a, but I canNOT figure out b. Can someone please explain? :)I need to know how to do this for my final next week.
as usual,
r^2 = x^2+y^2
r%2 = 9
r=3
y/r = sinθ
3/3 = sinθ
θ = π/2
so, we get (3,π/2)
y/r!! That makes much more sense! Someone else had told me y/x, so that's why it didn't work. Thanks!
To find the polar coordinates of a point given its rectangular coordinates, you can use the formulas:
r = √(x^2 + y^2), where r is the distance from the origin to the point, and
θ = arctan(y / x), where θ is the angle the line connecting the origin and the point makes with the positive x-axis.
Let's solve for point b with rectangular coordinates (0,3):
Step 1: Calculate the distance from the origin to the point.
r = √(0^2 + 3^2) = √(0 + 9) = √9 = 3
Step 2: Calculate the angle the line makes with the positive x-axis.
θ = arctan(3 / 0)
However, in this case, we encounter a problem. When x is equal to 0, we cannot compute the arctan(y / x) as it is undefined.
Therefore, we conclude that the point (0,3) has undefined polar coordinates since it lies on the y-axis and does not correspond to a unique angle.