There's nothing here that tells you that you need to use some technique from algebra explicitly as far as I can see?
Edit: I misread. See my follow up comment too.
The usual trig functions like sine and cosine are famous examples of transcendental functions so I very seriously doubt there is some clever algebra trick you're missing that the author intends you to do.
I'd assume your instructor (or the author) is expecting you to use your geometric knowledge about the unit circle on these if you haven't covered inverse trig functions yet. But I also can't really read their mind, so your best bet might be to just directly ask them?
Edit: This could also depend on what trigonometric identities you know so far too.