Determine if the following statement makes sense.
After plotting the point the rectangular coordinates (0,-4) a student found polar coordinates without having to show any form.
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The given statement is that a student plotted the point with rectangular coordinates (0, -4) and found its polar coordinates without showing any form.
To determine if the statement makes sense, we need to understand the process of converting rectangular coordinates to polar coordinates.
In rectangular coordinates, a point is represented by its x- and y-coordinates on a Cartesian plane. In polar coordinates, a point is represented by its distance from the origin (r) and the angle it forms with the positive x-axis (θ).
To convert rectangular coordinates to polar coordinates, the following formulas are used:
r = √(x^2 + y^2)
θ = atan2(y, x)
Applying these formulas to the given point (0, -4):
r = √(0^2 + (-4)^2) = √(0 + 16) = 4
θ = atan2(-4, 0) = undefined
We encounter a problem when calculating the angle (θ) because the division by zero occurs in the atan2 function, as the x-coordinate is 0. This means that the angle cannot be determined.
Based on this analysis, it does not make sense that the student found polar coordinates for the point (0, -4) without showing any form, as the angle cannot be determined.
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