Graph r=2sin(x)

Problem

r=2*sin(θ)

Solution

1. Identify the type of polar equation. The equation r=2*a*sin(θ) represents a circle in polar coordinates.

2. Determine the diameter and center. In the form r=2*a*sin(θ) the diameter is 2*a Here, 2*a=2 so the diameter is 2 and the radius is 1

3. Locate the orientation. Since the function is sin(θ) and the coefficient is positive, the circle is symmetric with respect to the vertical axis (θ=π/2 and lies above the pole (origin).

4. Find key points to plot. At θ=0 r=0 At θ=π/2 r=2 At θ=π r=0

5. Convert to rectangular coordinates to verify. Using r2=x2+y2 and y=r*sin(θ) we multiply the original equation by r to get r2=2*r*sin(θ) which becomes x2+y2=2*y

6. Complete the square for the rectangular form. x2+(y−1)2=1 This confirms a circle centered at (0,1) with radius 1

Final Answer

r=2*sin(θ)⇒x2+(y−1)2=1

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