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

Problem

(2,−2√(,3))

Solution

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

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

r=√(,(2)2+(−2√(,3))2)

r=√(,4+12)

r=√(,16)

r=4

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

tan(θ)=(−2√(,3))/2

tan(θ)=−√(,3)

4. Identify the quadrant of the point (2,−2√(,3)) Since x>0 and y<0 the point lies in Quadrant IV.

5. Find the angle θ in Quadrant IV where tan(θ)=−√(,3)

θ=(5*π)/3

Final Answer

(2,−2√(,3))=(4,(5*π)/3)

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