Convert to Polar Coordinates (-3,3)

Problem

(−3,3)

Solution

1. Identify the Cartesian coordinates (x,y) where x=−3 and y=3

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

r=√(,(−3)2+3)

r=√(,9+9)

r=√(,18)

r=3√(,2)

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

tan(θ′)=|3/(−3)|

tan(θ′)=1

θ′=π/4

4. Find the polar 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

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

Final Answer

(−3,3)=(3√(,2),(3*π)/4)

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