When is $\theta$ obtuse or acute in sin, cosine, tan when they are positive, negative or both? My textbook gives a non intuitive answer and tells us to memorize when the ratios are positive or negative or both based on some arbitrary rule that I don't understand.

I know how to do both of them, i just don't understand them fully yet. I think it has something to do with the unit circle? Not sure. 
 A: 
Define $\sin \theta = y$, $\cos \theta = x$, and $\tan \theta = \frac{y}{x}$ in terms of the right triangle in the unit circle.
Then you can see that when $\theta$ is acute, then the point $P$ lies in the first quadrant, so both $x$ and $y$ are positive, so $\sin \theta$, $\cos \theta$, and $\tan \theta$ are all positive.
On the other hand, when $\theta$ is obtuse, the point $P$ is in the second quadrant, so $x$ is negative and $y$ is positive, so $\cos \theta$ is negative and $\sin \theta$ is positive, but $\tan \theta$ is negative.
You can continue this for the third and fourth quadrants.
A: ANSWER
Teacher mostly tell us the tricks to find answer to such type of problems but after reading my answer, you might have the answer of Why they are?.
It seems that you need to understand the concept of $\sin, \cos$ and $\tan$
To understand what sine, cosine and tangent are you have to understand the term "function" in criteria of Mathematics.
I would like to provide the definition of rule form of function because I think it is an intuitive one.
Definition:

A function is a rule that produces a correspondence between two sets of elements such that to each element in the first set there corresponds one and only one element  in the second set
The first set is called domain and the second one is called range.
It is usually denoted by the symbol $f$

Think function as a machine in which we input some data, it executes the process and give it to us in the form of output.

For Instance:
let $f(x)=2x$
then, $f(0)=0$,
$f(i)=2i$,
$f(3)=6$
Don't think that $f$ is some constant and being multiplied by $x$ but it is the notation. May be you would have problem with the notation as Richard Feynman had but later he agreed to use the standard notations and so you should do otherwise you would have to face bigger problems in future. So, What have you noticed thus far? Can you see that we are plugging numbers in function and getting different output every time. So this is an intuitive approach to functions.
Now, finally, we shall draw our attention towards the origin of angular functions i.e. from where they came.
Trigonometric or Angular Functions:
There are basically two circular functions namely, sine and cosine. Others are ratios in terms of both of them or either of them ($\tan {\theta}=\frac{\sin{\theta}}{\cos{\theta}}$)

We choose a 2-D coordinate system so that this general angle ($\angle POM$) in above figure) is in standard position. In figure a unit circle (circle of radius 1) is drawn with center at the origin O. The terminal ray (${PO}$) of the angle cuts the circle at $P(x,y)$. Thus to every real number $\theta$, there corresponds a unique point $P(x,y)$
So the set of ordered pairs $[\theta ,(x,y)]$ defines a function with,
$domain=({\theta | \theta \in \mathbb R})$
and,
$range=[(x,y) | x^2+y^2=1, x,y \in \mathbb R]$
So,
$p(\theta)=(x,y)$ where $\theta \in \mathbb R$
i.e., $[(x,y)|x^2+y^2=1, x, y \in \mathbb R]$
We define $\sin[p(\theta)]$ by,
$\sin{\theta}=y$
and similarly,
$\cos{\theta}=x$
These functions are called trigonometric or circular or angular functions.
In general if the 2nd figure not contains a unit circle, then we define
$\sin{\theta}=\frac{y}{\overline{OP}}$
and $\cos{\theta}=\frac{x}{\overline{OP}}$
A: Personally I remember the shapes of the curves of the functions, which up to two right-angles look like this 
 
