Convert to Polar Coordinates (-2 square root of 3,2)

Problem

(−2√(,3),2)

Solution

1. Identify the Cartesian coordinates (x,y) where x=−2√(,3) and y=2

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

r=√(,(−2√(,3))2+(2)2)

r=√(,12+4)

r=√(,16)

r=4

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

tan(θ)=2/(−2√(,3))

tan(θ)=−1/√(,3)

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

5. Solve for θ in the correct quadrant. The reference angle is π/6 In Quadrant II, θ=π−π/6

θ=(5*π)/6

Final Answer

(x,y)=(−2√(,3),2)⇒(r,θ)=(4,(5*π)/6)

Want more problems? Check here!