Embedded Files
Objectives (click/tap to expand)
Use multiple-angle identities (primarily double-angle identities)
Use half-angle identities to evaluate trigonometric functions
Use power-reducing identities (You'll address as needed in Calculus)
All Trigonometric Identities
All Trigonometric Identities
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.
5-4 Double Angle Identities
5-4 Double Angle Identities
Watch before Day #51 lesson
Watch before Day #51 lesson
When trig functions of 2x, such as sin(2x), appear in the same equation as trig functions of x, such as cos(x), your very first priority needs to be getting the whole equation to include only trig functions of x. From there, apply techniques of earlier lessons. Here's what that looks like...
5-4 Half Angle Identities, continued
5-4 Half Angle Identities, continued
Optional for Day #51
Optional for Day #51
This video is about solving trigonometric equations which involve trig functions of half-angles (e.g. sin(x/2)) alongside trig functions of the full angle (e.g. cos(x)). We will address this topic in class, but consider watching if you still need more reinforcement or examples.
5-4 Double/Half Angle Identities, continued
5-4 Double/Half Angle Identities, continued
Day #52, no video
Day #52, no video
Most of the quadratic equations you get asked to solve in Math classes are able to be factored. Here is an example of a quadratic trig equation that cannot be factored. Click on the image to see a worked out solution. This is about as ugly as a trig equation will ever get in PreCalc, so if you can hang with this you're in great shape! The homework assignment for this lesson features at least one exercise with a quadratic that cannot be factored.
Solutions to selected exercises in Ch. 5.4
Solutions to selected exercises in Ch. 5.4
Here I show six different ways of working through exercise #45 in the assignment corresponding to this lesson (using all three versions of the tangent half-angle identity).
Here are my worked-out solutions to the exercises in Chapter 5.4 that I expect caused the most struggle. 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.
Upcoming Assessment Chapter 5.1, 5.3, 5.4
Upcoming Assessment Chapter 5.1, 5.3, 5.4
The next assessment will have a very similar format as the last one -- refer back to the preview of that last assessment. Most of the content will be the same too (simplifying trig expressions, solving trig equations, sum & difference formulas). You will receive a sheet of "Advanced" identities from Chapter 5.3, but you will still be responsible for knowing the "Fundamental" identities from Chapter 5.1 on your own. You will need to prepare for:
Everything from last assessment on Ch 5.1 & 5.3
Proving an identity (5.3)
Combining two sinusoids into one. e.g. rewrite 9sin(3x) - 5cos(3x) in the form A sin(Bx+C)+D. (end of 5.3)
Double-Angle Identities (5.4)
Half-Angle Identities (5.4)
Solving equations with solutions that are NOT special angles → require inverse trig (5.4 exercise #10, exercise #46, class exercise 1, class exercise 2)
Here are some extra practice trig equations from another various sources. Solutions start on the second page. Since the section of questions taken from another textbook only include odd answers, use a calculator to graphically check any even questions you choose to try. Certainly come by office hours if you have any troubles.
Go to next page, Chapter 5.5.
Page updated
Google Sites
Report abuse