Convert to Polar Coordinates (2,-2)

Problem

(2,−2)

Solution

1. Identify the Cartesian coordinates x and y from the given point (x,y)=(2,−2)

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

r=√(,2+(−2)2)

r=√(,4+4)

r=√(,8)

r=2√(,2)

3. Determine the angular coordinate θ using the formula tan(θ)=y/x

tan(θ)=(−2)/2

tan(θ)=−1

4. Identify the quadrant of the point (2,−2) Since x>0 and y<0 the point lies in Quadrant IV.

θ=arctan(−1)

θ=−π/4

5. Express the point in polar form (r,θ)

Final Answer

(2,−2)=(2√(,2),−π/4)

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