Find the Reference Angle (7pi)/3

Problem

(7*π)/3

Solution

1. Identify the given angle θ=(7*π)/3 and determine if it is within the standard range of [0,2*π]

2. Find a coterminal angle by subtracting 2*π from the original angle since (7*π)/3>2*π

(7*π)/3−2*π=(7*π)/3−(6*π)/3

(7*π)/3−(6*π)/3=π/3

3. Determine the quadrant of the coterminal angle π/3 Since 0<π/3<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/3

Final Answer

θ′=π/3

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