Question

If you were given a radian e.g. 3pi/4, how were you to know whether to use sin, tan or cos when finding the exact answer?

Answer 1

I tried this:

Explanation:

Sine, Cossine and Tangent are three "operations" exactly as sum, subtraction or multiplication or better, the square root...the only difference is that they operate on angles in a subtle and somewhat weird way.

It is weird because they relate the sides of a right triangle through the value they give you...ok it is complicated but I'll try with a diagram:

I used a different angle only to introduce the idea; now let us see with a bigger angle like the one you suggested. We can take our right triangle again but inside another structure.
In general Sine, Cossine and Tangent have a "geometrical" meaning that can be seen on a special structure called Unit Circle (of radius `r=1`)...have a look:

I am not sure I answered your question or I was clear enough...I hope so!