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Chapter 7: Problem 93

Explain how to convert from a rectangular equation to a polar equation.

Short Answer

Expert verified
To convert from a rectangular equation to a polar equation, simply replace \(x\) and \(y\) in the rectangular equation with \(r \cos(\theta)\) and \(r \sin(\theta)\) respectively and then simplify the equation as necessary to obtain the polar coordinate representation of the equation.

Step by step solution

01

Infer the relationships between rectangular and polar coordinates

Firstly, it's crucial to understand the link between the rectangular and polar coordinate systems. In the circular equation \((x^2 + y^2 = r^2)\) \(r^2\) could be replaced by \(x^2 + y^2\). Likewise, \(x\) could be replaced by \(r \cos(\theta)\) and \(y\) by \(r \sin(\theta)\) respectively in our equation.
02

Substitute the values into your equation

The second stage involves replacing each variables in the rectangular equation with their corresponding polar coordinates.
03

Simplify the result

The last phase is to simplify the equation, if possible, for a more succinct polar equation. You might want to manipulate or reduce the equation by applying some algebraic or trigonometric techniques.

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Most popular questions from this chapter

Explaining the Concepts Describe the test for symmetry with respect to the polar axis.

Use a graphing utility to graph the polar equation. $$r=\frac{1}{3-2 \sin \theta}$$

In Exercises \(69-76,\) find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex fifth roots of \(-1+i\)

In Exercises \(81-86,\) solve equation in the complex number system. Express solutions in polar and rectangular form. $$ x^{3}-(1+i \sqrt{3})=0 $$

Explain how to find the quotient of two complex numbers in polar form.
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