Objectives (click/tap to expand)
Use basic identities to evaluate expressions
Use basic identities to simplify expressions
Combine fractions and simplify expressions
Use factoring to simplify
Solve equations
Use Pythagorean identities to convert expressions
Here is a formula sheet for all the trig identities we will learn this year, for your convenience.
The first page has the Fundamental Identities. Think of this sheet as a set of "training wheels" that you will eventually need to learn to do without. These are the formulas that I keep insisting need to make sense -- they shall not simply be memorized. You will be expected to know all of them for the assessments.
The second page has the Advanced Identities. You will eventually need to know how to use all of them, but I make no claims that these should be self-evident in any way. So, I will provide a sheet of only the Advanced Identities for your assessments.
The first in a long list of "Identities" that need to make sense to you. You may be able to skip about 6 minutes of this video. If the first example is pristinely clear to you, then jump to the exercises in the last thirty seconds of the video. If seeing a slightly-more complicated problem worked out would help, jump back to 15:30 for the second example.
Using Trig Identities (and Algebra!) to simplify trig expressions
If you would like to see the "You Do" exercises worked out, watch this video
Here I show four different ways of working through exercise #35 in the assignment corresponding to this lesson. Obviously the diligent student will attempt that exercise first without any aid, but I do invite you to check these solutions out after you give it a shot. Even though not all the approaches are ones I would recommend, I believe it would still be useful for you to see the various ways that algebra and trig identities work together to simplify expressions and solve equations.
Unlike an Identity that is true for all inputs (except when one or both sides of the equation is undefined), many trig equations are true for only certain values of the input. Our job is to find which input values make such equations true.
If you would like to see the "You Do" exercise worked out, watch this video
Here's a little extra practice on simplifying trig expressions and solving trig equations. Answers on the second page. This if from another textbook so the wording/format is a bit different from our text, but it's still good practice.
Be aware that there are always multiple ways of approaching any trig exercise. I chose the approach that I find to be most efficient using methods that you've been taught, but you may find another perfectly valid approach.
Go to next page, Chapter 5.3.