Convert to Polar Coordinates (-2,3)

Problem

(−2,3)

Solution

1. Identify the Cartesian coordinates (x,y) as x=−2 and y=3

2. Calculate the radius r using the formula r=√(,x^2+y^2)

r=√(,(−2)^2+3^2)

r=√(,4+9)

r=√(,13)

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

tan(θ^′)=3/2

θ^′=arctan(3/2)

4. Determine the quadrant of the point. Since x<0 and y>0 the point lies in Quadrant II.

5. Find the polar angle θ for Quadrant II using θ=π−θ^′ (in radians) or θ=180^∘−θ^′ (in degrees).

θ=π−arctan(3/2)

6. State the polar coordinates in the form (r,θ)

Final Answer

(−2,3)=(√(,13),π−arctan(3/2))

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