Convert to Polar Coordinates (4,-4)

Problem

(4,−4)

Solution

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

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

r=√(,4+(−4)2)

r=√(,16+16)

r=√(,32)

r=4√(,2)

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

tan(θ)=(−4)/4

tan(θ)=−1

4. Find the value of θ by considering the quadrant. Since x>0 and y<0 the point is in Quadrant IV.

θ=arctan(−1)

θ=−π/4

5. Express the polar coordinates in the form (r,θ)

Final Answer

(4,−4)=(4√(,2),−π/4)

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