Problem 6 - Calculus Early Transcendentals

Question

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

Step-by-Step Solution

Answer

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

Step 1: Write down the given Cartesian equation

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

Step 2: Express y in terms of polar coordinates

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

Step 3: Solve for r

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

Step 4: Write the final polar equation

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