Welcome to Trigonometry !!!!

Trigonometry is the branch of mathematics dealing with the relationship between side lengths and angle measures of triangles.

Specifically, the Trigonometric Ratios tell us the ratio between two specific sides of a (RIGHT) triangle, given an angle.

We have already seen Trigonometric ratios at play when we looked at the 30 - 60 and 45 -45 right triangles last class.

In the 30 -60 Right Triangle, trigonometric ratios tell us that from the

angle, the relationship between the side opposite the

angle (short leg) compared to the hypotenuse is a 1:2 ratio. We will soon define this trigonometric ratio as the SINE ratio.

Your calculator can give you the values of all relations (side ratios), given any angle angle measure. You can use Trig ratios to solve for missing sides or angles of a (right) triangle given some information. For the most part this is just writing and solving proportions for similar triangles (where one ratio is the TRIG ratio and the other ratio is a ratio comparing two sides of the given triangle.)

SOHCAHTOA

For the three main (basic) TRIG ratios will be using: we will use the acronym --> SOHCAHTOA . For these basic trig ratios we will be using RIGHT TRIANGLES ONLY.

SINE =

COSINE =

TANGENT =

Before we attempt to write a TRIG ratio, it is SOOOO important to correctly label the SIDES of the right triangle

Always label the HYPOTENUSE first -->It should be the easiest because it is always opposite the right angle.

Now, the OPPOSITE and ADJACENT side depend where

is located.

("theta") is a greek symbol we use in Trigonometry to indicate which angle we are using to establish the ratios.

Personally, I like to locate the OPPOSITE first --> it is located OPPOSITE

. Then the last side remaining is the ADJACENT side.

Let's practice identifying the sides together on the next slide before we work on our own.