alpha = PI - 5/8 PI
alpha = 3/8 PI
The angle 5/8 Pi is found in the second quadrant.
The reference angle for any angle (A) in the second quadrant is given by
[tex]\begin{gathered} A_r=180-A \\ \\ A_r=\pi-A\text{ (In radian)} \end{gathered}[/tex]
Therefore, we can solve for 5/8 Pi:
[tex]\begin{gathered} A_r=\pi-\frac{5}{8}\pi \\ \therefore A_r=\frac{3}{8}\pi \end{gathered}[/tex]
But in order to put it in the box in the question:
[tex]\begin{gathered} \alpha=PI\text{ - }\frac{5\pi}{8} \\ \\ \alpha=\frac{3}{8}\text{ PI} \end{gathered}[/tex]
alpha = PI - 5/8 PI
alpha = 3/8 PI
