Convert to Polar Coordinates (2,-3)

Problem

(2,−3)

Solution

1. Identify the Cartesian coordinates (x,y) where x=2 and y=−3

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

r=√(,2+(−3)2)

r=√(,4+9)

r=√(,13)

3. Calculate the angle θ using the formula θ=arctan(y/x) Since the point (2,−3) is in the fourth quadrant, the angle will be between (3*π)/2 and 2*π (or between −π/2 and 0.

θ=arctan((−3)/2)

θ≈−0.9828* radians

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

Final Answer

(2,−3)=(√(,13),arctan(−3/2))

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