Answer
$ a.\quad \approx 0.841068670568$
$b.\quad\approx-0.729727656227$
$c.\quad\approx 0.463647609001$
Work Step by Step
$ a.\quad$
The online calculator at desmos returns $0.841068670568$
when we type $arcsec(1.5)$
If your calculator can't do this, enter $\displaystyle \cos^{-1}(\frac{1}{1.5})$
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 $-0.729727656227$
when we type $arccsc(-1.5)$
If your calculator can't do this, enter $\displaystyle \sin^{-1}(-\frac{1}{1.5})$
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 $0.463647609001$
when we type $arccot(2)$
If your calculator can't do this, enter $\displaystyle \tan^{-1}(-\frac{1}{1.5})$
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,$\displaystyle \quad y=\tan(\frac{1}{x})$
