Find the Reference Angle (15pi)/7

Problem

(15*π)/7

Solution

1. Identify the given angle θ=(15*π)/7 and determine its position relative to a full rotation of 2*π radians.

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

(15*π)/7−2*π=(15*π)/7−(14*π)/7

(15*π)/7−(14*π)/7=π/7

3. Determine the quadrant of the coterminal angle π/7 Since 0<π/7<π/2 the angle is in Quadrant I.

4. Apply the reference angle rule for Quadrant I, which states that the reference angle θ′ is equal to the angle itself.

θ′=π/7

Final Answer

Reference Angle of (15*π)/7=π/7

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