Convert to Polar Coordinates (-8,8)

Problem

(−8,8)

Solution

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

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

r=√(,(−8)2+8)

r=√(,64+64)

r=√(,128)

r=8√(,2)

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

tan(θ)=8/(−8)

tan(θ)=−1

4. Find the reference angle and adjust for the quadrant. Since x<0 and y>0 the point lies in Quadrant II.

θ=arctan(−1)+π

θ=−π/4+π

θ=(3*π)/4

Final Answer

(x,y)=(−8,8)⇒(r,θ)=(8√(,2),(3*π)/4)

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