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: