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Chapter 6: Problem 33

Polar coordinates of a point are given. Find the rectangular coordinates of each point. $$\left(4,90^{\circ}\right)$$

Short Answer

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

Step by step solution

01

Identify given polar coordinates

The polar coordinates given are \((4,90^{\circ})\). Therefore, \(r = 4\) and \(\theta = 90^{\circ}\).
02

Convert Angle to Radians

First, we have to ensure that the given angle \(\theta\) is in radians before using it in formula. Given that \(\theta = 90^{\circ}\), to convert to radians we multiply by \(\frac{\pi}{180}\). So, \(\theta = 90^{\circ} * \frac{\pi}{180} = \frac{\pi}{2}\) radians.
03

Use the conversion formulas

Next, using the formulas for conversion, we find \(x = r \cdot \cos(\theta) = 4 * \cos\left(\frac{\pi}{2}\right) = 0\), and \(y = r \cdot \sin(\theta) = 4 * \sin\left(\frac{\pi}{2}\right) = 4\).

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Most popular questions from this chapter

Describe a test for symmetry with respect to the line \(\theta=\frac{\pi}{2}\) in which \(r\) is not replaced.

Find \(\text {pro}_{\mathbf{w}} \mathbf{V}\) Then decompose v into two vectors, \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2},\) where \(\mathbf{v}_{1}\) is parallel to \(\mathbf{w}\) and \(\mathbf{v}_{2}\) is orthogonal to \(\mathbf{w}.\) $$\mathbf{v}=2 \mathbf{i}+\mathbf{j}, \quad \mathbf{w}=6 \mathbf{i}+3 \mathbf{j}$$

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