Problem

Find polar coordinates of the point that has rectangular coordinates $(-5,-5)$. Write your answer using degrees. Polar coordinates: $\left(\square=\square^{\circ}\right)$

Solution

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 \(\boxed{(7.07, 225^\circ)}\)

From Solvely APP
Source: https://solvelyapp.com/problems/20067/

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