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

r=√(,8+(−8)2)

r=√(,64+64)

r=√(,128)

r=8√(,2)

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

tan(θ)=(−8)/8

tan(θ)=−1

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

θ=arctan(−1)

θ=−π/4

5. Express the angle in the standard interval [0,2*π) if necessary.

θ=2*π−π/4

θ=(7*π)/4

Final Answer

(8,−8)⇒(8√(,2),(7*π)/4)

Want more problems? Check here!