Convert to Polar Coordinates (- square root of 3,1)

Problem

(−√(,3),1)

Solution

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

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

r=√(,(−√(,3))2+(1)2)

r=√(,3+1)

r=2

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

tan(θ)=1/(−√(,3))

4. Find the reference angle and the quadrant. Since x<0 and y>0 the point lies in Quadrant II.

θ=arctan(1/(−√(,3)))+π

θ=−π/6+π

θ=(5*π)/6

Final Answer

(−√(,3),1)=(2,(5*π)/6)

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