Find the Reference Angle (13pi)/5

Problem

(13*π)/5

Solution

1. Identify the given angle θ=(13*π)/5 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 until the result is between 0 and 2*π

(13*π)/5−2*π=(13*π)/5−(10*π)/5

(13*π)/5−(10*π)/5=(3*π)/5

3. Determine the quadrant for the coterminal angle (3*π)/5 Since π/2<(3*π)/5<π the angle lies in Quadrant II.

4. Apply the reference angle formula for Quadrant II, which is θ′=π−θ

θ′=π−(3*π)/5

5. Simplify the expression to find the final reference angle.

θ′=(5*π)/5−(3*π)/5

θ′=(2*π)/5

Final Answer

Reference Angle of (13*π)/5=(2*π)/5

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