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

Problem

(6,−6√(,3))

Solution

1. Identify the Cartesian coordinates (x,y) from the given point where x=6 and y=−6√(,3)

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

r=√(,6+(−6√(,3))2)

r=√(,36+108)

r=√(,144)

r=12

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

tan(θ)=(−6√(,3))/6

tan(θ)=−√(,3)

4. Identify the quadrant to find the correct value for θ Since x>0 and y<0 the point lies in Quadrant IV.

θ=arctan(−√(,3))

θ=−π/3

5. Express the angle in the standard interval [0,2*π) if required by adding 2*π

θ=−π/3+2*π

θ=(5*π)/3

Final Answer

(6,−6√(,3))=(12,(5*π)/3)

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