on equations between rectangular and polar coordinates are as follows (th x = r cos 0, y=r sin 0 p2 = x² + y, tan 0 = P(x, y) t two conversion equations above to re-label the vertical and horizontal legs of this right triangle in terms of r and O only. Then explain or he Pythagorean theorem still works in your newly re-labeled triangle.

on equations between rectangular and polar coordinates are as follows (th x = r cos 0, y=r sin 0 p2 = x² + y, tan 0 = P(x, y) t two conversion equations above to re-label the vertical and horizontal legs of this right triangle in terms of r and O only. Then explain or he Pythagorean theorem still works in your newly re-labeled triangle.

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter8: Complex Numbers And Polarcoordinates

Section: Chapter Questions

Problem 7GP

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Question

The conversion equations between rectangular and polar coordinates are as follows (th
the text):
x = r cos 0, y=r sin 0
p2 = x² + y?, tan 0 =
P(x, y)
Use the first two conversion equations above to re-label the vertical and horizontal legs of this right triangle in terms of r and 0 only. Then explain or
show how the Pythagorean theorem still works in your newly re-labeled triangle.

Expert Solution

Step 1

Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the squares of the vertical leg and the horizontal leg in a right triangle.