Search
Algebraic Solutions to Graphical Trig Problems?
![](https://mander.xyz/pictrs/image/74983f65-0ae3-47db-9dca-90a551140be1.jpeg?format=webp&thumbnail=128)
![](https://mander.xyz/pictrs/image/74983f65-0ae3-47db-9dca-90a551140be1.jpeg?format=webp)
I've been knocking out the trig problems in this section with minimal difficulty so far, but I've run straight into a brick wall on this "Algebraic" part. I'm asked to find sin(x)=0 between [0,2π). If I graphed the unit circle this would be a trivial exercise to show sin(θ)=0 when θ=0 or π.
Where I have trouble is- I'm very explicitly being told here that the solution is ALGEBRAIC, and I'm struggling to figure out a way to rearrange sin(x)=0 to come up with the known answer. Further, unit circles are not in this chapter, they wouldn't likely ask me to exercise a skill taught in another chapter. What am I missing?
It's not just 31, either. Looking ahead at eg 37, I can easily show sin(-x) = -sin(x) on a unit circle. I could maybe fuck around with inverse trig ratios but those are in section 3- this is only section 1.
Help me out here, drop a hint, share a link: how do I solve sin(x)=0 on [0,2π), but algebraically? I suspect it's something glaringly obvious and/or very very simple I've overlooked.
Inverse Trig Functions Not Giving Consistent Outputs With Each Other?
![](https://mander.xyz/pictrs/image/1d51a7ac-dd43-4f9a-923f-87a925b376eb.jpeg?format=webp&thumbnail=128)
![](https://mander.xyz/pictrs/image/1d51a7ac-dd43-4f9a-923f-87a925b376eb.jpeg?format=webp)
It's homework help, but I'm not asking for the solution. The problem only asks for cos, sin, tan, cot, csc given sec. I found those pretty quickly on my own, and confirmed solutions with the back of the book.
Where I run into confusion is when I try to find angle theta on my own. Arccos of found cos gives 2.06, arcsin of found sin gives 1.08, and arctan of found tan gives -1.08. Problem givens exclude possibility of the negative angle found by arctan(-15/8), but the other two are possible and conflicting. And why wouldn't they all be the same? I reattempted because there were so many erase marks from trying to figure this out that it was almost illegible.
Am I wrong? Did the book give me a point not on the unit circle or something, assuming I wouldn't try to find theta on my own? Have I used arcfuncs wrong- I checked the domains against the function definitions? Have I found a hole in math?