Convert to Polar Coordinates (5,-5)

Problem

(5,−5)

Solution

1. Identify the Cartesian coordinates (x,y) where x=5 and y=−5

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

r=√(,5+(−5)2)

r=√(,25+25)

r=√(,50)

r=5√(,2)

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

tan(θ)=(−5)/5

tan(θ)=−1

4. Identify the quadrant of the point (5,−5) Since x>0 and y<0 the point lies in Quadrant IV.

5. Solve for θ in the interval [0,2*π) or (−π,π] In Quadrant IV, the angle whose tangent is −1 is (7*π)/4 or −π/4

θ=(7*π)/4

Final Answer

(5,−5)⇒(5√(,2),(7*π)/4)

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