Find the Reference Angle (17pi)/4

Problem

(17*π)/4

Solution

1. Identify the given angle θ=(17*π)/4

2. Find a coterminal angle within the interval [0,2*π) by subtracting multiples of 2*π

3. Calculate the subtraction:

(17*π)/4−2*π=(17*π)/4−(8*π)/4=(9*π)/4

4. Subtract another 2*π because the angle is still greater than 2*π

(9*π)/4−2*π=(9*π)/4−(8*π)/4=π/4

5. Determine the reference angle θ′ based on the quadrant. Since π/4 is in the first quadrant (0<π/4<π/2, the reference angle is equal to the angle itself.

Final Answer

θ′=π/4

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