Answer
$ a.\quad \approx 1.91063323625$
$ b.\quad\approx 0.628874925495$
$ c.\quad\approx 2.67794504459$
Work Step by Step
$ a.\quad$
The online calculator at desmos returns $1.91063323625$
when we type $arcsec(-3)$
If your calculator can't do this, enter $\displaystyle \cos^{-1}(-\frac{1}{3})$
The reason for this is that
$y=\sec^{-1}x$ is the number in $[0, \pi/2$) $\cup(\pi/2, \pi$] for which $\sec y=x.$
This means that$\displaystyle \quad \frac{1}{\cos y}=x$,
Or,$\displaystyle \quad \cos y=\frac{1}{x}$
So,$\displaystyle \quad y=\cos^{-1}(\frac{1}{x})$
$ b.\quad$
The online calculator at desmos returns $0.628874925495$
when we type $arccsc(1.7)$
If your calculator can't do this, enter $\displaystyle \sin^{-1}(\frac{1}{1.7})$
The reason for this is that
$y=\csc^{-1}x$ is the number in $[-\pi/2,0) \cup(0, \pi/2]$ for which $\csc y=x.$
This means that$\displaystyle \quad \frac{1}{\sin y}=x$,
Or,$\displaystyle \quad \sin y=\frac{1}{x}$
So,$\displaystyle \quad y=\sin^{-1}(\frac{1}{x})$
$ c.\quad$
The online calculator at desmos returns $2.67794504459$
when we type $arccot(-2)$
If your calculator can't do this, enter $\displaystyle \tan^{-1}(-\frac{1}{2})$
The result is negative, $-0.463647609001$
so we add $\pi$ to force the result into the interval $(0, \pi).$
The reason for this is that
$y=\cot^{-1}x$ is the number in $(0, \pi)$ for which $\cot y=x.$
This means that$\displaystyle \quad \frac{1}{\tan y}=x$,
Or,$\displaystyle \quad \tan y=\frac{1}{x}$
So,$\displaystyle \quad y=\tan(\frac{1}{x})$
(it has to belong to the interval $(0,\pi)$ so we add $\pi$ if negative)
