Graph r=3sin(x)

Problem

r=3*sin(θ)

Solution

1. Identify the type of polar equation. The equation r=a*sin(θ) represents a circle in polar coordinates.

2. Determine the diameter and orientation. Since the function is sin(θ) and the coefficient is 3 the circle has a diameter of 3 and is symmetric with respect to the vertical axis (θ=π/2.

3. Find the center and radius. In the Cartesian plane, this circle is centered at (0,1.5) with a radius of 1.5

4. Plot key points to visualize the curve. At θ=0 r=0 At θ=π/2 r=3 At θ=π r=0

5. Sketch the graph. The graph starts at the origin, moves upward to its peak at (3,π/2) and returns to the origin, forming a circle sitting on the polar axis.

Final Answer

r=3*sin(θ)

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