Find the Reference Angle (13pi)/6

Problem

(13*π)/6

Solution

1. Identify the given angle θ=(13*π)/6 and determine if it is within the standard range of [0,2*π]

2. Find the coterminal angle by subtracting 2*π from the given angle since (13*π)/6>2*π

(13*π)/6−2*π=(13*π)/6−(12*π)/6

(13*π)/6−(12*π)/6=π/6

3. Determine the quadrant of the coterminal angle π/6 Since 0<π/6<π/2 the angle lies in Quadrant I.

4. Calculate the reference angle θ′ For an angle in Quadrant I, the reference angle is equal to the angle itself.

θ′=π/6

Final Answer

Reference Angle of (13*π)/6=π/6

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