Convert to Polar Coordinates (-6 square root of 3,6)

Problem

(−6√(,3),6)

Solution

1. Identify the Cartesian coordinates (x,y) as x=−6√(,3) and y=6

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

r=√(,(−6√(,3))2+6)

r=√(,36*(3)+36)

r=√(,108+36)

r=√(,144)

r=12

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

tan(θ)=6/(−6√(,3))

tan(θ)=−1/√(,3)

4. Identify the quadrant to find the correct value of θ Since x<0 and y>0 the point is in Quadrant II.

θ=arctan(−1/√(,3))+180

θ=−30+180

θ=150

5. Convert to radians if necessary.

θ=150⋅π/180

θ=(5*π)/6

Final Answer

(x,y)=(−6√(,3),6)⇒(r,θ)=(12,(5*π)/6)

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