Problem

The polar coordinates of a point are $(-5, \pi)$. Find the rectangular coordinates of this point. The rectangular coordinates are (Simplify your answer. Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed. Use integers or fractions for any numbers in the expression.)

Solution

Step 1 :The polar coordinates are given as $(-5, \pi)$. The conversion from polar coordinates $(r, \theta)$ to rectangular coordinates $(x, y)$ is given by the formulas $x = r \cos(\theta)$ and $y = r \sin(\theta)$. We can use these formulas to find the rectangular coordinates.

Step 2 :Let's substitute the given values into the formulas. We have $r = -5$ and $\theta = \pi$.

Step 3 :Calculating $x$ gives us $x = -5 \cos(\pi) = 5$.

Step 4 :Calculating $y$ gives us $y = -5 \sin(\pi) = 0$.

Step 5 :So, the rectangular coordinates are $(5, 0)$.

Step 6 :Final Answer: The rectangular coordinates of the point are \(\boxed{(5, 0)}\).

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Source: https://solvelyapp.com/problems/24077/

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