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For $\sin z = 1$: $z = 90^\circ$.
For $\sin z = \frac{1}{2}$: $z = 30^\circ, 150^\circ$.
Thus, solutions are $30^\circ, 90^\circ, 150^\circ$.
\boxed{30^\circ}, \boxed{90^\circ}, \boxed{150^\circ}
$$Question: A science educator is designing a probability-based game for elementary students using a fair 10-sided die (numbered 1 through 10). If a student rolls the die four times, what is the probability that exactly two of the rolls result in a number greater than 7?
To solve this, we use the **binomial probability formula**, since each die roll is independent, and we're interested in a specific number of successes (rolling a number greater than 7) in a fixed number of trials (4 rolls).
Numbers greater than 7 on a 10-sided die: 8, 9, 10 → 3 outcomes
Probability of success (rolling >7): $ p = \frac{3}{10} = 0.3 $
Probability of failure (rolling ≤7): $ 1 - p = 0.7 $
Number of trials $ n = 4 $