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Chapter 6: Problem 37

Polar coordinates of a point are given. Find the rectangular coordinates of each point. $$\left(-4, \frac{\pi}{2}\right)$$

Short Answer

Expert verified
The rectangular coordinates of the point are (0,-4).

Step by step solution

01

Identify the polar coordinates

Recognize that the given point \((-4, \frac{\pi}{2})\) has polar coordinates r = -4 and 胃 = \frac{\pi}{2}. Polar coordinates are usually given in the format (r, 胃).
02

Apply the transformation formulas

Use the formulas \(x = r \cos(\theta)\) and \(y = r \sin(\theta)\) to convert the polar coordinates to rectangular coordinates. Here, r = -4 and 胃 = \(\frac{\pi}{2}\). Plug these values into the formulas to get: \(x = -4 \cos(\frac{\pi}{2})\) and \(y = -4 \sin(\frac{\pi}{2})\).
03

Calculate the rectangular coordinates

We know that \(\cos(\frac{\pi}{2}) = 0\) and \(\sin(\frac{\pi}{2}) = 1\). So, we get: \(x = -4 * 0 = 0\) and \(y = -4 * 1 = -4\).

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