# Sine

In trigonometry, we shall use a new symbol, , called theta, to represent an unknown angle.

In geometry and trigonometry we have a convention.

We label the vertices of the triangle *A*, *B* and *C*.

And we label the sides of the triangle *a*, *b* and *c*, where

side *a* is opposite angle *A*

side *b* is opposite angle *B*

side *c* is opposite angle *C*

Suppose that we have a right angled triangle, as shown above.

*AB* is called the hypotenuse, it is opposite the right angle, and it is always the longest side.

The side *BC* is opposite , it is called the opposite side.

*AC*, the remaining side, is called the adjacent side.

Now we introduce 3 new functions.

Note that

That is

If we use the naming convention *A*, *B*, *C*, *a*, *b*, *c*; the triangle becomes

and

sin() is read "sine of theta" or "sine theta"

cos() is read "cosine of theta" or "cos of theta" or "cosine theta" or "cos theta"

tan() is read "tan of theta" or "tan theta"

sin(), cos() and tan() are functions of , they depend on .

As changes, sin(), cos() and tan() change.

sin(), cos() and tan() are ratios of lengths, they are just numbers, decimals.