Convert to Polar Coordinates (-4,-4)

Problem

(−4,−4)

Solution

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

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

r=√(,(−4)2+(−4)2)

r=√(,16+16)

r=√(,32)

r=4√(,2)

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

tan(θ′)=|(−4)/(−4)|

tan(θ′)=1

θ′=π/4

4. Find the actual angle θ by observing that the point (−4,−4) lies in the third quadrant.

θ=π+θ′

θ=π+π/4

θ=(5*π)/4

Final Answer

(x,y)=(−4,−4)⇒(r,θ)=(4√(,2),(5*π)/4)

Want more problems? Check here!