Chapter+14+Notes

We will now build on our abilities with the trig values and learn to use them to simplify expressions. This chapter will be presented in two parts. Part one will be sections 1, 6, and 7 and will deal with trig identities. Part 2 will be over sections 2, 3, 4, and 5 and will cover ways of solving equations with trig.

In section 1 of this chapter we are intorduced to trig identities and how to use them to prove relations. These take practice and creativity but they are all possible.

We can find more identities iin section 6. These are the Co-function, Negative Angle, and the Sum and Difference Identities. These will expand the number of and types of angles that we can find exact values of.

Another set of useful identities are the Double - Angle and Half - Angle Identities that are found in Section 7. These will often times be used to confirm trig values that we already know.

Here is a list of the identities that we have studied in this chapter. This list is very helpful when it comes to working with simplifying trigonometric values.

Part 2 of Chapter 14 deals with our ability to solve equations that invlove trig functions. This will give us the ability to find angle measurements when we know the sine, cosine, or tangent value of the angle. Also we will learn some new rules and relations among the sides and angles of triangles, including an expansion of the Pythagorean Theorem.

In this section we learn how to use acrsines, arccosines, and arctangents. These are used to undo the basic trig relations that we know. This will allow us to solve equations that involve trig functions.

This section is a bit of a step back. Here we are using the basic trig ratios learned in Geometry to solve problems.

In this section we learn a set of formulas to help find the area of triangles and to find different side lengths and angle measurements. These processes are based on a system called the Law of Sines.

We will now conclude our study of Algebra 2 with an expansion of the Pythagorean Theorem called the Law of Cosines. This in conjunction with the Law of Sines will make it possible to find missing parts of triangles in nearly all situations.