Find the Reference Angle (19pi)/3

Problem

(19*π)/3

Solution

1. Identify the given angle θ=(19*π)/3

2. Find the coterminal angle within the range [0,2*π) by subtracting multiples of 2*π

3. Calculate the number of full rotations:

(19*π)/3=6*π+π/3

4. Subtract 6*π (which is 3×2*π to find the coterminal angle:

(19*π)/3−6*π=π/3

5. Determine the quadrant of the coterminal angle π/3 Since 0<π/3<π/2 the angle is in Quadrant I.

6. Apply the reference angle rule for Quadrant I, where the reference angle θ′ is equal to the angle itself.

θ′=π/3

Final Answer

Reference Angle of (19*π)/3=π/3

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