Find the Quadrant of the Angle pi/12

Problem

π/12

Solution

1. Identify the angle in radians and the boundaries for each quadrant in the coordinate plane.

2. Compare the given angle π/12 to the standard quadrant boundaries: Quadrant I is 0<θ<π/2 Quadrant II is π/2<θ<π Quadrant III is π<θ<(3*π)/2 and Quadrant IV is (3*π)/2<θ<2*π

3. Determine the relationship between π/12 and the first boundary π/2 by finding a common denominator.

4. Observe that π/2=(6*π)/12

5. Conclude that since 0<π/12<(6*π)/12 the angle lies within the first quadrant.

Final Answer

π/12∈Quadrant I

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