Convert to Polar Coordinates (4,6)

Problem

(4,6)

Solution

1. Identify the Cartesian coordinates (x,y) where x=4 and y=6

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

r=√(,4+6)

r=√(,16+36)

r=√(,52)

r=2√(,13)

3. Calculate the angle θ using the formula θ=arctan(y/x) Since the point is in the first quadrant, no adjustment is needed.

θ=arctan(6/4)

θ=arctan(3/2)

θ≈0.9828* radians

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

Final Answer

(4,6)=(2√(,13),arctan(3/2))

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