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

Problem

(−3√(,3),−3)

Solution

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

2. Calculate the radius r using the formula r=√(,x^2+y^2)

r=√(,(−3√(,3))^2+(−3)^2)

r=√(,27+9)

r=√(,36)

r=6

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

tan(θ^′)=|(−3)/(−3√(,3))|

tan(θ^′)=1/√(,3)

θ^′=π/6

4. Find the actual angle θ by observing that the point (−3√(,3),−3) lies in Quadrant III, where θ=π+θ^′

θ=π+π/6

θ=(7*π)/6

Final Answer

(−3√(,3),−3)=(6,(7*π)/6)

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