Convert to Polar Coordinates (3,3)

Problem

(3,3)

Solution

1. Identify the Cartesian coordinates (x,y) where x=3 and y=3

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

r=√(,3+3)

r=√(,9+9)

r=√(,18)

r=3√(,2)

3. Calculate the angle θ using the formula θ=arctan(y/x) Since the point is in the first quadrant, the reference angle is the actual angle.

θ=arctan(3/3)

θ=arctan(1)

θ=π/4

4. Express the result in the polar coordinate form (r,θ)

Final Answer

(3,3)⇒(3√(,2),π/4)

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