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

Problem

(2√(,3),−2)

Solution

1. Identify the Cartesian coordinates (x,y) from the given point.

x=2√(,3)

y=−2

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

r=√(,(2√(,3))2+(−2)2)

r=√(,12+4)

r=√(,16)=4

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

tan(θ′)=|(−2)/(2√(,3))|

tan(θ′)=1/√(,3)

θ′=π/6

4. Find the actual angle θ based on the quadrant. Since x>0 and y<0 the point is in Quadrant IV.

θ=2*π−π/6

θ=(11*π)/6

Final Answer

(2√(,3),−2)=(4,(11*π)/6)

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