Convert to Polar Coordinates (-2,2 square root of 3)

Problem

(−2,2√(,3))

Solution

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

2. Calculate the radius r using the formula r=√(,x^2+y^2)

r=√(,(−2)^2+(2√(,3))^2)

r=√(,4+12)

r=√(,16)

r=4

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

tan(θ^′)=|(2√(,3))/(−2)|

tan(θ^′)=√(,3)

θ^′=π/3

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

θ=π−θ^′

θ=π−π/3

θ=(2*π)/3

Final Answer

(−2,2√(,3))=(4,(2*π)/3)

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