Find the Reference Angle (13pi)/3

Problem

(13*π)/3

Solution

1. Identify the given angle θ=(13*π)/3

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

3. Calculate the subtraction:

(13*π)/3−2*π=(13*π)/3−(6*π)/3=(7*π)/3

4. Subtract another 2*π because the angle is still greater than 2*π

(7*π)/3−2*π=(7*π)/3−(6*π)/3=π/3

5. Determine the reference angle θ′ based on the quadrant. Since π/3 is in the first quadrant (0<π/3<π/2, the reference angle is equal to the angle itself.

Final Answer

θ′=π/3

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