9. sketch the graph of the following polar equation.\n$$\\cos \\theta = \\frac{6}{r}$$
9. sketch the graph of the following polar equation.\n$$\\cos \\theta = \\frac{6}{r}$$
Answer
Explanation:
Step1: Rearrange the polar equation
Multiply both sides by $r$ to isolate the terms. $$r \cos \theta = 6$$
Step2: Convert to rectangular coordinates
Use the standard conversion formula $x = r \cos \theta$. $$x = 6$$
Step3: Identify the geometric shape
The equation $x = 6$ represents a vertical line in the Cartesian plane.
Step4: Describe the graph
The graph is a vertical line passing through $(6, 0)$ on the x-axis.
Answer:
The graph of the polar equation $\cos \theta = \frac{6}{r}$ is a vertical line defined by the rectangular equation $x = 6$. To sketch it, draw a straight vertical line that intersects the polar axis (x-axis) at the point $(6, 0)$.