Convert to Polar Coordinates (3,(2pi)/3)

Problem

(3,(2*π)/3)

Solution

1. Identify the given coordinates as polar coordinates (r,θ) where r=3 and θ=(2*π)/3

2. Apply the formula for the xcoordinate, x=r*cos(θ)

x=3*cos((2*π)/3)

3. Evaluate the cosine function at (2*π)/3 which is −1/2

x=3*(−1/2)=−3/2

4. Apply the formula for the ycoordinate, y=r*sin(θ)

y=3*sin((2*π)/3)

5. Evaluate the sine function at (2*π)/3 which is √(,3)/2

y=3*(√(,3)/2)=(3√(,3))/2

6. Combine the results into the rectangular coordinate pair (x,y)

Final Answer

(3,(2*π)/3)=(−3/2,(3√(,3))/2)

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