Convert to Polar Coordinates (5,120)

Problem

(5,120)

Solution

1. Identify the given coordinates as rectangular coordinates (x,y) where x=5 and y=120

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

r=√(,5+120)

r=√(,25+14400)

r=√(,14425)

r=5√(,577)

3. Determine the angular coordinate θ using the formula θ=arctan(y/x) Since x>0 the point is in the first quadrant.

θ=arctan(120/5)

θ=arctan(24)

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

Final Answer

(5,120)=(5√(,577),arctan(24))

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