QuestionNow consider $h(x)=\tan \left(\frac{\pi}{4}(x+\pi / 6)\right)+3$ (a) (2 points) Compute $h(0), h(\pi / 6), h(\pi / 2)$.

Studdy Solution
Simplify the expression:
$$h(\pi / 2) = \tan \left(\frac{\pi}{4} \cdot \frac{2\pi + \pi}{6}\right) + 3$$ $$h(\pi / 2) = \tan \left(\frac{\pi}{4} \cdot \frac{3\pi}{6}\right) + 3$$ $$h(\pi / 2) = \tan \left(\frac{\pi^2}{8}\right) + 3$$
Since $\frac{\pi^2}{8}$ is not a standard angle, we approximate $\tan\left(\frac{\pi^2}{8}\right)$ as a small angle, which is approximately $\frac{\pi^2}{8}$.
$$h(\pi / 2) \approx \frac{\pi^2}{8} + 3$$
The values are:
$$h(0) \approx \frac{\pi^2}{24} + 3$$ $$h(\pi / 6) \approx \frac{\pi^2}{12} + 3$$ $$h(\pi / 2) \approx \frac{\pi^2}{8} + 3$$