Answer:
2.29 rad
Explanation:
The terminal arm of an angle in standard position passes through the point:
[tex](-7,8)[/tex]
For an angle in standard position, its angle in degrees:
[tex]\begin{gathered} \theta=\arctan\left(\frac{y}{x}\right) \\ \implies\theta=\arctan\left(\frac{8}{-7}\right)=-48.81 \end{gathered}[/tex]
Since (-7, 8) is in Quadrant II:
[tex]\theta=180-48.81=131.19\degree[/tex]
Finally, convert the result to radians:
[tex]\theta=131.19\times\frac{\pi}{180}=2.29\text{ rad}[/tex]
The radian value of the angle in the interval (0, 2π) correct to the nearest hundredth is 2.29 radians.
