Convert to Polar Coordinates (1,-1)

Problem

(1,−1)

Solution

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

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

r=√(,1+(−1)2)

r=√(,1+1)

r=√(,2)

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

tan(θ)=(−1)/1

tan(θ)=−1

4. Find the value of θ by considering the quadrant. Since x>0 and y<0 the point is in the fourth quadrant.

θ=arctan(−1)

θ=−π/4

5. Express the coordinates in the standard polar form (r,θ)

(r,θ)=(√(,2),−π/4)

Final Answer

(1,−1)=(√(,2),−π/4)

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