Convert to Rectangular Coordinates (-4,(2pi)/3)

Problem

(−4,(2*π)/3)

Solution

1. Identify the given polar coordinates (r,θ) where r=−4 and θ=(2*π)/3

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

x=−4*cos((2*π)/3)

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

x=−4*(−1/2)=2

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

y=−4*sin((2*π)/3)

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

y=−4*(√(,3)/2)=−2√(,3)

Final Answer

(r,θ)=(−4,(2*π)/3)⇒(x,y)=(2,−2√(,3))

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