Quiz 7.8:
Question:
5th Ed: #35
One of the following statements is always true; the other is true for some values of x and not for others. Which is which? Justify your answer with an example.
I) \( \arcsin(\sin x)=x \)
II) \( \sin ( \arcsin x )=x \)
II) \( \sin ( \arcsin x )=x \)
5th Ed: #35
Solution:
Statement I is only true for \( -\frac{\pi}{2} \leq x \leq \frac{\pi}{2} \) because the range of the inverse sine function is \( -\frac{\pi}{2} \leq x \leq \frac{\pi}{2} \). So for example \( \arcsin(\sin 2\pi)= \arcsin(0) = 0 \neq 2\pi \)
Statement II is always true.
Statement II is always true.
