Convert to Polar Coordinates (0,2)

Problem

(0,2)

Solution

1. Identify the given rectangular coordinates (x,y) where x=0 and y=2

2. Calculate the radial distance r using the formula r=√(,x2+y2)

r=√(,0+2)

r=√(,4)

r=2

3. Determine the polar angle θ by observing the position of the point on the Cartesian plane. Since x=0 and y is positive, the point lies on the positive y-axis.

θ=π/2

4. Verify using the tangent relationship tan(θ)=y/x Since x=0 the tangent is undefined, which corresponds to θ=π/2 for a positive y value.

Final Answer

(0,2)⇒(2,π/2)

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