Convert to Polar Coordinates (-4 square root of 3,4)

Problem

(−4√(,3),4)

Solution

1. Identify the Cartesian coordinates (x,y) where x=−4√(,3) and y=4

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

r=√(,(−4√(,3))2+(4)2)

r=√(,16*(3)+16)

r=√(,48+16)

r=√(,64)

r=8

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

tan(θ′)=|4/(−4√(,3))|

tan(θ′)=1/√(,3)

θ′=π/6

4. Find the actual angle θ by observing 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

(−4√(,3),4)=(8,(5*π)/6)

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