The mistake in the table is located at point [tex](r, \theta) = \left(4.24, \frac{\pi}{4} \right)[/tex].
How to evaluate a function with respect to a given table
In this question we must evaluate the function [tex]r(\theta) = 1 + 2\cdot \sin \theta[/tex], where [tex]\theta[/tex] in radians, for all [tex]\theta[/tex] set in the table and looks that all values of [tex]r[/tex] match with all corresponding values in the table.
According to the table, [tex]r\left(\frac{\pi}{4} \right) = 4.24[/tex] but the evaluation of the function brings out a different result:
[tex]r\left(\frac{\pi}{4} \right) = 1 + 2\cdot \sin \frac{\pi}{4}[/tex]
[tex]r\left(\frac{\pi}{4} \right) = 1 + 2\cdot \left(\frac{\sqrt{2}}{2} \right)[/tex]
[tex]r\left(\frac{\pi}{4} \right) = 1 + \sqrt{2}[/tex]
[tex]r\left(\frac{\pi}{4} \right) \approx 2.414[/tex]
The mistake in the table is located at point [tex](r, \theta) = \left(4.24, \frac{\pi}{4} \right)[/tex]. [tex]\blacksquare[/tex]
To learn more on polar functions, we kindly invite to check this verified question: https://brainly.com/question/9547138
