Convert to Rectangular Coordinates (2,pi/3)

Problem

(2,π/3)

Solution

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

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

x=2*cos(π/3)

3. Evaluate the cosine function, knowing cos(π/3)=1/2

x=2⋅1/2=1

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

y=2*sin(π/3)

5. Evaluate the sine function, knowing sin(π/3)=√(,3)/2

y=2⋅√(,3)/2=√(,3)

Final Answer

(2,π/3)=(1,√(,3))

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