Step 1 :Given a point with rectangular coordinates (-5,-5), we can find the polar coordinates using the following formulas:
Step 2 :\(r = \sqrt{x^2 + y^2}\)
Step 3 :\(\theta = \arctan\left(\frac{y}{x}\right)\)
Step 4 :However, since the point is in the third quadrant, we need to add 180 degrees to the angle.
Step 5 :Let's calculate the polar coordinates for the point (-5,-5).
Step 6 :\(x = -5\)
Step 7 :\(y = -5\)
Step 8 :\(r = \sqrt{(-5)^2 + (-5)^2} = 7.07\)
Step 9 :\(\theta = \arctan\left(\frac{-5}{-5}\right) = 45.0\)
Step 10 :Since the point is in the third quadrant, we add 180 degrees to the angle: \(\theta = 45.0 + 180 = 225.0\)
Step 11 :The polar coordinates of the point (-5,-5) are approximately (7.07, 225) in degrees.
Step 12 :Final Answer: The polar coordinates of the point (-5,-5) are approximately \(\boxed{(7.07, 225^\circ)}\)