Convert to Rectangular Coordinates (6,30)

Problem

(6,30)

Solution

1. Identify the given polar coordinates (r,θ) where r=6 and θ=30

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

3. Substitute the values into the formula: x=6*cos(30)

4. Evaluate the cosine function: x=6⋅√(,3)/2=3√(,3)

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

6. Substitute the values into the formula: y=6*sin(30)

7. Evaluate the sine function: y=6⋅1/2=3

Final Answer

(6,30)=(3√(,3),3)

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