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

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 polar angle θ by identifying the quadrant. Since x<0 and y>0 the point lies in Quadrant II.

θ=π−θ′

θ=π−π/6

θ=(5*π)/6

Final Answer

(x,y)=(−3√(,3),3)⇒(r,θ)=(6,(5*π)/6)

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