Convert to Polar Coordinates (-2,2)

Problem

(−2,2)

Solution

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

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

r=√(,(−2)2+(2)2)

r=√(,4+4)

r=√(,8)

r=2√(,2)

3. Determine the reference angle θ′ using the formula tan(θ′)=|y/x|

tan(θ′)=|2/(−2)|

tan(θ′)=1

θ′=π/4

4. Find the actual angle θ by identifying the quadrant. Since x<0 and y>0 the point lies in Quadrant II.

θ=π−θ′

θ=π−π/4

θ=(3*π)/4

Final Answer

(x,y)=(−2,2)⇒(r,θ)=(2√(,2),(3*π)/4)

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