Convert to Polar Coordinates (4,1)

Problem

(4,1)

Solution

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

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

r=√(,4+1)

r=√(,16+1)

r=√(,17)

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

θ=arctan(1/4)

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

Final Answer

(4,1)=(√(,17),arctan(1/4))

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