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)2+5)

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. Since x<0 and y>0 the point lies in Quadrant II.

5. Find the angle θ in Quadrant II where tan(θ)=−1

θ=(3*π)/4

Final Answer

(x,y)=(−5,5)⇒(r,θ)=(5√(,2),(3*π)/4)

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