# Analytic Trigonometry

## What is Analytic Trigonometry? (Definition)

**Analytic trigonometry** is the branch of mathematics that examines trigonometric identities in terms of their positions on the *x*-*y* plane.

## Why Study Analytic Trigonometry?

Trigonometry is used to solve many topics in engineering and science.

The identities that we learn in this
chapter will help us to **simplify and solve problems** that we meet later. You can see how we use some of this knowledge in Uses of
Trigonometry.

## What's in this Chapter?

1. Proving trigonometric identities reminds you of the basic trigonometric ratios and then shows you how to go about **proving identities**.

2. Sin, cos tan of Sum of Two Angles shows you how to expand out expressions like sin(*α* + *β*) and cos(*α* − *β*).

3 Double Angle Formulas explains about expressions like `sin\ 2α` and `cos\ 2α` and their equivalents.

4. Half Angle Formulas explains how to find and use expressions like `sin(alpha/2)`, with equivalents.

5. Solving trigonometric equations has several worked examples of problems like: **Solve **`sin\ 2θ = 0.8`.

6. Expressing *a* sin *θ* ± *b* cos *θ* in the form *R* sin(*θ* ± *α*) is very useful when we need to simplify the sum of a sine and cosine expression, where the period is the same for each.

7. Graphs of Inverse Trigonometric Functions shows you how to graph functions like *y* = arccos *x*.

The graph of `y="arccsc"\ x`, which we meet in 7. Graphs of Inverse Trigonometric Functions.

We start the chapter with the section on Fundamental Trigonometric Identities ».