Trigonometry in right triangles is really just a way of labelling the sides of the triangle and the fractions you can make out of them.
For example, consider this right triangle:
Each of the sides of a right triangle has a name, and each of these fractions you can make from the sides has a name!
Let's look at a simple right triangle, with one of the angles marked .
The sides are named according to where the marked angle is.
The side called 'Hypotenuse' is always the long side across from the right angle.
The side called 'Opposite' is always across from, or 'opposite' to, the marked angle .
The side called 'Adjacent' is the one next to, or 'adjacent' to, .
Now let's make the fractions from the named sides:
Here is the interesting part: each one of these fractions has its own name!
Here are the names of the fractions you can make from the sides of a right triangle:
Mathematicians being generally lazy sorts of people wanted an easy way to remember these fraction names, and a quicker way to write them:
These can be remembered by using the first letter from each name, to make the acronym:
O.K., now you know what the words mean...
, or , just means:
"The fraction you get when you divide the adjacent side of a right triangle by the hypotenuse".
Now lets actually work out the sin, cos, and tan fractions for a few triangles.
Move on to the second page.