Convert to Polar Coordinates (-3,pi/6)

Problem

(−3,π/6)

Solution

1. Identify the given coordinates as polar coordinates (r,θ) where r=−3 and θ=π/6 The task is to find an equivalent representation, typically with a positive radius r>0

2. Apply the rule for negative radii in polar coordinates, which states that (−r,θ) is equivalent to (r,θ+π)

3. Calculate the new radius by taking the absolute value of the original radius.

r=|−3|=3

4. Calculate the new angle by adding π to the original angle.

θ=π/6+π

5. Simplify the angle by finding a common denominator.

θ=π/6+(6*π)/6=(7*π)/6

Final Answer

(−3,π/6)=(3,(7*π)/6)

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