Learning $\arcsin, \arccos, \arctan$ - how to? Sorry for asking such question.
I have a very basic understanding of $\arcsin, \arccos, \arctan$ functions. I do know how their graph looks like and not much more beyond that.
Calculate:

Which specific keywords should I google to learn how to solve the following tasks? I think those aren't equations (googling 'cyclometric equations' was a dead end). Perhaps you would like to share with some link to a beginner-friendly learning source?
Thank you.
 A: Some good reference as summary from Wikipedia are


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*List of trigonometric identities
and also


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*Inverse trigonometric functions
Some exercises given requires only to calculate the value for the functions at some point, other else are more tricky and you need to acquire a deeply understanding of the matter.
Refer also to the related


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*Reference Request: Book for Trigonometry and Geometry

*Good book on advanced trig
A: I would say there are three things you are expected to do on this list.  One is to know the trig functions of special angles, so for 4 you should know that $\tan \frac \pi 4=1,$ so $\arctan 1=\frac \pi 4$  Watch out for the ranges specified for the inverse trig functions.  Second is that $\sin(\arcsin (x))=x$.  When you have $\arcsin (\sin(x))$ you may be shifted by factors of $\pi$.  Finally when you have $\sin(\arccos(\frac 13))$ draw a right triangle with $\cos$ of one angle $\frac 13$, so it is a $1-\sqrt 8-3$ triangle and find the sine of the angle, here $\frac 13\sqrt 8$.
A: This lecture has been particularly helpful on understanding the subject:
https://academics.utep.edu/Portals/1788/CALCULUS%20MATERIAL/4_7%20INVERSE%20TRIG%20FNS.pdf
