TRIGONOMETRY
Trigonometry is the study of triangles. In this topic, we’re going to focus on three trigonometric functions that specifically concern right-angled triangles. They are: sine, cosine, and tangent, which get shortened to sin, cos, and tan.
To define what these 3 functions, we first have to understand how to label the sides of right-angled triangle:
- Firstly, the hypotenuse is always the longest side; it is the one opposite the right-angle.
- The other two sides depend on where the angle you’re working with is. The names are quite explanatory:
the opposite side is the side that is opposite to the angle
the adjacent side is the side that is adjacent (next to) the angle.
Now we define the 3 functions to be:
These are 3 extremely useful functions because they give us a way of relating the angles in a right-angled triangle to the side-lengths.
They can be used to find both missing angles and side-lengths.
Now, it´s your turn. Do the exercises, finding x in each triangle below and check your answers: