Convert to Polar Coordinates (3,-3)

Problem

(3,−3)

Solution

1. Identify the Cartesian coordinates (x,y) where x=3 and y=−3

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

r=√(,3+(−3)2)

r=√(,9+9)

r=√(,18)

r=3√(,2)

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

tan(θ)=(−3)/3

tan(θ)=−1

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

θ=arctan(−1)

θ=−π/4

θ=(7*π)/4

Final Answer

(3,−3)⇒(3√(,2),(7*π)/4)

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