Problem 69 - Algebra and Trigonometry

Question

Use a graphing utility to graph the polar equation. $$r=\frac{3}{\cos \theta}$$

Step-by-Step Solution

Answer

The graph of the equation \(r = \frac{3}{\cos(\theta)}\) is a vertical line crossing the point at x = 3 in Cartesian coordinates

Step 1: Conversion from Polar to Cartesian

Convert the polar equation \(r = \frac{3}{\cos(\theta)}\) into Cartesian equation with the relation \(r^2 = x^2 + y^2\) and \(x = r\cos(\theta)\). Substituting these into the polar equation, we get: x = 3.

Step 2: Plotting the Graph

Use a graphing utility to plot the Cartesian equation. The equation 'x = 3' represents a vertical line passing through (3,0) on the x-axis.

Step 3: Final Verification

Ensure that your graph is a vertical line passing through the point (3,0) on the x-axis to verify the success of the translation and the graphing process.