Convert to Rectangular Coordinates (5,pi/3)

Problem

(5,π/3)

Solution

1. Identify the given polar coordinates as (r,θ) where r=5 and θ=π/3

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

3. Substitute the values into the x equation:

x=5*cos(π/3)

4. Evaluate the cosine of π/3 which is 1/2

x=5⋅1/2=5/2

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

6. Substitute the values into the y equation:

y=5*sin(π/3)

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

y=5⋅√(,3)/2=(5√(,3))/2

Final Answer

(5,π/3)=(5/2,(5√(,3))/2)

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