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Chapter 6: Problem 99

Polar coordinates of a point are given. Use a graphing utility to find the rectangular coordinates of each point to three decimal places. $$(-4,1.088)$$

Short Answer

Expert verified
The rectangular coordinates for the given polar coordinates are approximately \((-1.760, -3.592)\)

Step by step solution

01

Converting the Polar Coordinates to Rectangular Coordinates

The first step is to take the polar coordinates, \((-4,1.088)\), and plug them into the formulas for \(x\) and \(y\). \(x = r \cdot cos(\theta) = -4 \cdot cos(1.088)\) and \(y = r \cdot sin(\theta) = -4 \cdot sin(1.088)\).
02

Evaluating the Functions

Next, both \( \cos(1.088)\) and \( \sin(1.088)\) must be evaluated. Calculating these, we find \( \cos(1.088) \approx 0.440\) and \( \sin(1.088) \approx 0.898 \).
03

Final Calculation

Finally, we need to compute \(x\) and \(y\) using the results from the immediate previous step. Thus, \(x = -4 \cdot 0.440 = -1.760 \)and \(y = -4 \cdot 0.898 = -3.592\). As a point in the rectangular coordinate system, this provides us \((-1.760,-3.592)\). To three decimal places, the values round to \((-1.760, -3.592)\).

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