The rectangular coordinates of a point are given. Find two sets of polar coordinates for the point.
(-3,-3)
tanØ = y/x = -3/-3 = 1
Ø = π/4
x = rcosØ = (1/√2)r
-3 = (1/√2)r
r = -3√2
one is (-3√2,π/4)
I will let you find the other
To find the polar coordinates for a given point, we need to use the formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
Given the rectangular coordinates (-3, -3), we can substitute these values into the formulas to find the polar coordinates.
1. First, let's find the value of r:
r = √((-3)^2 + (-3)^2)
r = √(9 + 9)
r = √18 = 3√2
2. Next, let's find the value of θ:
θ = arctan((-3)/(-3))
θ = arctan(1)
θ = π/4 (in radians) or 45° (in degrees)
So, our first set of polar coordinates for the point (-3, -3) is (3√2, π/4).
3. Now, let's consider a second set of polar coordinates. Since we are dealing with a point in the third quadrant, we need to add π (180°) to our angle θ.
θ2 = θ + π
θ2 = π/4 + π
θ2 = 5π/4 (in radians) or 225° (in degrees)
So, our second set of polar coordinates for the point (-3, -3) is (3√2, 5π/4).