Convert to Polar Coordinates (-10,10)

Problem

(−10,10)

Solution

1. Identify the Cartesian coordinates (x,y) where x=−10 and y=10

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

r=√(,(−10)2+10)

r=√(,100+100)

r=√(,200)

r=10√(,2)

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

tan(θ)=10/(−10)

tan(θ)=−1

4. Find the quadrant to select the correct value for θ Since x<0 and y>0 the point lies in the second quadrant.

θ=arctan(−1)+180

θ=−45+180

θ=135

5. Convert to radians if necessary.

θ=(3*π)/4

Final Answer

(x,y)=(−10,10)⇒(r,θ)=(10√(,2),(3*π)/4)

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