Convert to Polar Coordinates (-6,6)

Problem

(−6,6)

Solution

1. Identify the Cartesian coordinates (x,y) where x=−6 and y=6

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

r=√(,(−6)2+6)

r=√(,36+36)

r=√(,72)

r=6√(,2)

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

tan(θ)=6/(−6)

tan(θ)=−1

4. Identify the quadrant of the point. Since x<0 and y>0 the point lies in Quadrant II.

θ=arctan(−1)+π

θ=−π/4+π

θ=(3*π)/4

5. Combine the values into the polar coordinate pair (r,θ)

Final Answer

(−6,6)=(6√(,2),(3*π)/4)

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