Evaluate (13pi)/4

Problem

(13*π)/4

Solution

1. Identify the angle as an improper fraction of π and determine its position on the unit circle by finding a coterminal angle within the range [0,2*π)

2. Subtract multiples of 2*π (which is (8*π)/4 from the given angle to find the coterminal equivalent.

(13*π)/4−2*π=(13*π)/4−(8*π)/4

(13*π)/4−(8*π)/4=(5*π)/4

3. Determine the quadrant of the angle (5*π)/4 Since π<(5*π)/4<(3*π)/2 the angle lies in Quadrant III.

4. Calculate the reference angle by subtracting π from the coterminal angle.

(5*π)/4−π=π/4

5. Evaluate the trigonometric position or convert to degrees if necessary. In degrees, the calculation is as follows:

(13*π)/4⋅180/π=13⋅45

13⋅45=585

Final Answer

(13*π)/4=585

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