Welcome from **She Loves Math! ** I know it’s been awhile, but I wanted to welcome everyone back to school and talk a little about **Trigonometry, **which is usually part of a **Pre-Calc** class these days.

I’ve completed the **Right Triangle Trigonometry**, **Graphs of Trig Functions**, **Transformations of Trig Functions** sections, and the beginning of the **Inverses of the Trigonometric Functions **section.

Here is an excerpt from my **Right Triangle Trigonometry** section to get you started with Trig:

You may have been introduced to Trigonometry in **Geometry**, when you had to find either a **side length** or **angle measurement** of a triangle. Trigonometry is basically the study of **triangles**, and was first used to help in the computations of astronomy. Today it is used in engineering, architecture, medicine, physics, among other disciplines.

The **6 basic trigonometric functions** that you’ll be working with are **sine**, **cosine**, **tangent**, **cosecant**, **secant**, and**cotangent**. (Don’t let the fancy names scare you; they really aren’t that bad).

With **Right Triangle Trigonometry**, we use the trig functions on **angles**, and get a **number** back that we can use to get a side measurement, as an example. Sometimes we have to work backwards to get the **angle measurement back** so we have to use what a call an **inverse trig function**. ** But basically remember that we need the trig functions so we can figure out triangles’ sides and angles that we don’t otherwise know. **

Later, we’ll see how to use trig to find areas of triangles, too, among other things.

You may have been taught **SOH – CAH – TOA (SOHCAHTOA)** to remember these. Back in the old days when I was in high school, we didn’t have **SOHCAHTOA**, nor did we have fancy calculators to get the values; we had to look up trigonometric values in tables.

Remember that the definitions below assume that the triangles are **right triangles**, meaning that they all have one **right angle**. Also note that in the following examples, our angle measurements are in **degrees**; later we’ll learn about another angle measurement unit, **radians**, which we’ll discuss here in the** Angles and Unit Circle section.**

## Basic Trigonometric Functions (SOH – CAH – TOA)

Here are the **6 trigonometric functions**, shown with both the SOHCAHTOA and **Coordinate System** Methods. Note that the second set of three trig functions are just the reciprocals of the first three; this makes it a little easier!

Note that the **cosecant** (**csc**), **secant** (**sec**), and **cotangent** (**cot**) functions are called **reciprocal functions**, or** reciprocal trig functions**, since they are the reciprocals of **sin**, **cos**, and **tan**, respectively.

For the coordinate system method, assume that the vertex of the angle in the triangle is at the origin (0, 0):

Keep checking back, as I’m trying to write every day, and please let me know if you have any questions or comments. Keep working hard! Lisa 🙂