(d) \( \sin \theta=1 \) (g) \( \sin \theta-0,574=0 \)

**(d)** Given the equation \[ \sin \theta = 1, \] we know that the sine function reaches its maximum value \(1\) only at an angle of \(\frac{\pi}{2}\) within the interval \([0, 2\pi)\). Because sine has a period of \(2\pi\), the general solution is \[ \theta = \frac{\pi}{2} + 2\pi k,\quad \text{where } k \in \mathbb{Z}. \] **(g)** The equation \[ \sin \theta - 0.574 = 0 \] can be rewritten as \[ \sin \theta = 0.574. \] Let \[ \alpha = \arcsin(0.574). \] Within a period, the sine function takes the value \(0.574\) at two angles: \[ \theta = \alpha \quad \text{and} \quad \theta = \pi - \alpha. \] Taking into account the periodicity of the sine function (period \(2\pi\)), the general solutions are: \[ \theta = \alpha + 2\pi k \quad \text{or} \quad \theta = (\pi - \alpha) + 2\pi k,\quad \text{where } k \in \mathbb{Z}. \]