Convert to Polar Coordinates (-11,11)

Problem

(−11,11)

Solution

1. Identify the Cartesian coordinates (x,y) where x=−11 and y=11

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

r=√(,(−11)2+11)

r=√(,121+121)

r=√(,242)

r=11√(,2)

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

tan(θ′)=|11/(−11)|

tan(θ′)=1

θ′=π/4

4. Find the actual angle θ by observing the quadrant. Since x<0 and y>0 the point is in Quadrant II.

θ=π−θ′

θ=π−π/4

θ=(3*π)/4

Final Answer

(x,y)=(−11,11)⇒(r,θ)=(11√(,2),(3*π)/4)

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