which restricted one - to - one trig function has a range of 0 ≤ y ≤ π and y ≠ π/2?\no y = arcsec x\no y =…

Answer:

1. A. $y = \arcsec x$
2. C. $y=\arcsin x$, E. $y = \arctan x$

Explanation:

Step1: Recall range of inverse - trig functions

The range of $y = \arccos x$ is $0\leq y\leq\pi$. The range of $y=\arcsin x$ is $-\frac{\pi}{2}\leq y\leq\frac{\pi}{2}$. The range of $y = \arcsec x$ is $0\leq y\leq\pi,y\neq\frac{\pi}{2}$. The range of $y=\arccsc x$ is $-\frac{\pi}{2}\leq y\leq\frac{\pi}{2},y\neq0$. The range of $y=\arctan x$ is $-\frac{\pi}{2}<y<\frac{\pi}{2}$. The range of $y = \text{arccot }x$ is $0 < y<\pi$.

Step2: Match ranges for first question

For the range $0\leq y\leq\pi$ and $y\neq\frac{\pi}{2}$, the function is $y = \arcsec x$.

Step3: Match ranges for second question

For the range $-\frac{\pi}{2}<y<\frac{\pi}{2}$, the functions are $y=\arcsin x$ and $y = \arctan x$.