Find the Reference Angle (7pi)/5

Problem

(7*π)/5

Solution

1. Determine the quadrant of the given angle θ=(7*π)/5 by comparing it to the axes.

2. Compare to π and (3*π)/2 to see that π<(7*π)/5<(3*π)/2 because (5*π)/5<(7*π)/5<(7.5*π)/5

3. Identify the quadrant as Quadrant III.

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

5. Subtract π from the given angle.

θ′=(7*π)/5−π

6. Find a common denominator to perform the subtraction.

θ′=(7*π)/5−(5*π)/5

7. Simplify the expression to find the reference angle.

θ′=(2*π)/5

Final Answer

Reference Angle of (7*π)/5=(2*π)/5

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