Questionple: Determine the values of $x, 0 \leq x \leq 3 \pi$ so that $y=4 \sin \left[\frac{2}{3}\left(x+\frac{\pi}{2}\right)\right]-5$ equals -3 . $$\left.3=4 \sin \frac{\left[2 / 3\left(x+\frac{\pi}{2}\right)\right.}{9}\right]-5$$
Period $=$

Studdy Solution
Find all solutions for $x$ within the range $0 \leq x \leq 3\pi$.
For $x = -\frac{\pi}{4} + 3k\pi$, solve for $k$:
$$0 \leq -\frac{\pi}{4} + 3k\pi \leq 3\pi$$
For $x = \frac{3\pi}{4} + 3k\pi$, solve for $k$:
$$0 \leq \frac{3\pi}{4} + 3k\pi \leq 3\pi$$
Calculate the values of $x$ for integer values of $k$ that satisfy these inequalities.
The values of $x$ that satisfy the equation within the given range are:
$$x = \frac{3\pi}{4}$$