Convert to Rectangular Coordinates (5,pi/6)

Problem

(5,π/6)

Solution

1. Identify the given polar coordinates (r,θ) where r=5 and θ=π/6

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

3. Substitute the values into the x formula:

x=5*cos(π/6)

4. Evaluate the cosine of π/6 which is √(,3)/2

x=5⋅√(,3)/2=(5√(,3))/2

5. Apply the formula for the ycoordinate, which is y=r*sin(θ)

6. Substitute the values into the y formula:

y=5*sin(π/6)

7. Evaluate the sine of π/6 which is 1/2

y=5⋅1/2=5/2

Final Answer

(5,π/6)=((5√(,3))/2,5/2)

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