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Chapter 6: Problem 96

Convert the polar equation to rectangular form. \(r=4 \csc \theta\)

Short Answer

Expert verified
The rectangular form of the polar equation \(r = 4 \csc \theta\) is \(\ y = 4\).

Step by step solution

01

Rewrite the Equation Using the Sine Function

We must know that the cosecant function is the reciprocal of the sine function. Hence, we can rewrite the equation \(r = 4 \csc \theta\) as \(r = \frac{4}{\sin \theta}\), which is equivalent to \(r \sin \theta = 4\).
02

Use the Rectangular-Polar Relation

Now use the rectangular-polar relationship \(y= r\sin \theta\). We substitute this into our equation from step 1 to get: \(y = 4\).
03

Write the Final Answer

The rectangular form of the equation is simply \(y = 4\). This is because when the polar equation is transformed to rectangular coordinates, the result is a horizontal line.

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