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Chapter 10: Problem 6

What is the polar equation of the horizontal line \(y=5 ?\)

Short Answer

Expert verified
Answer: The polar equation for the horizontal line y=5 is \(r = \frac{5}{\sin{\theta}}\).

Step by step solution

01

Write down the given Cartesian equation

The given horizontal line is \(y=5\).
02

Express y in terms of polar coordinates

Since \(y = r\sin{\theta}\), we can substitute this into the given equation: \(r\sin{\theta} = 5\).
03

Solve for r

We can solve for r by dividing both sides by \(\sin{\theta}\): \(r = \frac{5}{\sin{\theta}}\).
04

Write the final polar equation

The polar equation for the given horizontal line \(y=5\) is: \(r = \frac{5}{\sin{\theta}}\).

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