Convert to Polar Coordinates (-4,8)

Problem

(−4,8)

Solution

1. Identify the Cartesian coordinates (x,y) where x=−4 and y=8

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

r=√(,(−4)^2+8^2)

r=√(,16+64)

r=√(,80)

r=4√(,5)

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

tan(θ^′)=|8/(−4)|

tan(θ^′)=2

θ^′=arctan(2)

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

θ=π−arctan(2)

Final Answer

(−4,8)=(4√(,5),π−arctan(2))

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