Convert to Rectangular Coordinates (-7,(2pi)/3)

Problem

(−7,(2*π)/3)

Solution

1. Identify the given polar coordinates (r,θ) where r=−7 and θ=(2*π)/3

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

x=−7*cos((2*π)/3)

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

x=−7*(−1/2)

x=7/2

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

y=−7*sin((2*π)/3)

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

y=−7*(√(,3)/2)

y=−(7√(,3))/2

Final Answer

(−7,(2*π)/3)=(7/2,−(7√(,3))/2)

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