Question

Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°.

Answer 1

Make a drawing showing it using rectangular coordinates. For soie reason my draw feature is not working.

Note that you have a value equal to the \[\sqrt{5^{2} +(-5^{2})}=\sqrt{50}= 5\sqrt{2}\]
Now calculate the anngle down from the x axis (negative) using the sinverse sine of:\[5 \over 5\sqrt{2}\] which is 45 degrees. this means the polar coordinates are:
\[5\sqrt{2}at -45^{^{o}}\]and 315 degrees.