Find the polar coordinate of the following.
(0,-6)
I know r = sq.root of 6 but tan theta = -6/0 doesn't exist so how will I find the degree? Thanks
To find the polar coordinates of the point (0, -6), we need to determine both the magnitude (r) and angle (θ) in polar form.
First, let's find the magnitude (r). The magnitude is found by taking the square root of the sum of the squares of the x and y coordinates of the point. In this case, since the point is (0, -6), the magnitude (r) can be calculated as follows:
r = √(0^2 + (-6)^2)
= √(0 + 36)
= √36
= 6
Therefore, the magnitude (r) of the point (0, -6) is 6.
Now, we need to determine the angle (θ) in polar form. Since the x-coordinate is 0 and the y-coordinate is -6, we can conclude that the point lies on the negative y-axis.
However, as you correctly noted, the tangent function (tan θ) is undefined for θ = 90 degrees and 270 degrees. Therefore, we need to use the arctangent function (arctan or tan^(-1)) to determine the angle.
Let's calculate the arctangent of the ratio of the y-coordinate to the x-coordinate:
θ = arctan(-6/0)
The arctangent function returns an angle in the range of -90 degrees to 90 degrees, inclusive. So, the angle θ is either -90 degrees or 90 degrees.
Since the point lies on the negative y-axis, the angle is -90 degrees.
Therefore, the polar coordinate of the point (0, -6) is (r, θ) = (6, -90 degrees).