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Chapter 6: Problem 97

Polar coordinates of a point are given. Use a graphing utility to find the rectangular coordinates of each point to three decimal places. $$\left(4, \frac{2 \pi}{3}\right)$$

Short Answer

Expert verified
The rectangular coordinates of the given point in polar coordinates are approximately (-2, 3.464).

Step by step solution

01

Prepare the formula for conversion

Set up the appropriate formulas for conversion from polar coordinates to rectangular coordinates. We have two formulas: \(x = r\cos(\theta)\) for the x-coordinate and \(y = r\sin(\theta)\) for the y-coordinate.
02

Calculation of X-Coordinate

Insert the values into the formula for x-coordinate: \(x = 4\cos\left(\frac{2 \pi}{3}\right)\). After performing the calculation, the resulting value of x will be approximately -2.
03

Calculation of Y-Coordinate

Similarly, insert values into the formula for y-coordinate: \(y = 4\sin\left(\frac{2 \pi}{3}\right)\). Post calculation, we will get y approximately equals 3.464.

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