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 ».