9. sketch the graph of the following polar equation.\n\n\\(\\cos \\theta = \\frac{6}{r}\\)
9. sketch the graph of the following polar equation.\n\n\\(\\cos \\theta = \\frac{6}{r}\\)
Answer
Explanation:
Step1: Rewrite the polar equation
Start with the given polar equation (\cos\theta=\frac{6}{r}). Multiply both sides by (r) (assuming (r\neq0)) to get (r\cos\theta = 6).
Step2: Convert to rectangular coordinates
Recall the conversion formula (x = r\cos\theta). Substituting this into the equation from Step 1, we obtain (x = 6).
Step3: Identify the graph
The equation (x = 6) in rectangular coordinates represents a vertical line that is parallel to the (y)-axis and passes through the point ((6,0)) on the (x)-axis. To sketch it, draw a straight vertical line at (x = 6) on the coordinate plane.
Answer:
The graph of the polar equation (\cos\theta=\frac{6}{r}) is the vertical line (x = 6) (a straight vertical line passing through ((6,0)) and parallel to the (y)-axis).