Convert to Rectangular Coordinates (2,pi/6)

Problem

(2,π/6)

Solution

1. Identify the given polar coordinates (r,θ) where r=2 and θ=π/6

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

3. Substitute the values into the x equation:

x=2*cos(π/6)

4. Evaluate the cosine function:

x=2*(√(,3)/2)

x=√(,3)

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

6. Substitute the values into the y equation:

y=2*sin(π/6)

7. Evaluate the sine function:

y=2*(1/2)

y=1

Final Answer

(2,π/6)=(√(,3),1)

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