Convert to Polar Coordinates (3,60)

Problem

(3,60)

Solution

1. Identify the given rectangular coordinates (x,y) where x=3 and y=60

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

r=√(,3+60)

r=√(,9+3600)

r=√(,3609)

r=3√(,401)

3. Calculate the angular coordinate θ using the formula θ=arctan(y/x) Since the point is in the first quadrant (x>0,y>0, the reference angle is the actual angle.

θ=arctan(60/3)

θ=arctan(20)

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

Final Answer

(3,60)=(3√(,401),arctan(20))

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