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 distance r using the formula r=√(,x^2+y^2)

r=√(,(−1)^2+(1)^2)

r=√(,1+1)

r=√(,2)

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

tan(θ^′)=|1/(−1)|

tan(θ^′)=1

θ^′=π/4

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

θ=π−θ^′

θ=π−π/4

θ=(3*π)/4

Final Answer

(−1,1)⇒(√(,2),(3*π)/4)

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