Trigonometry


This web page will feature material exclusively devoted to the developments of ideas in triogonometry as such. For precalculus materials, please see that web page.

 


 

Trigonometry

Weeks 1 and 2


Trigonometry is generally taught in conjunction with a secondary algebra class. Here we are not going to do that. You can find the syllabus for the course here: Trigonometry syllabus

I also will be using material from this excellent book on trigonometry by Larson:

Larson & Falvo Trigonometry 8th txtbk

Here is the lecture for Tuesday July 28 — Lecture 3 Part A and Lecture 3 Part B

As promised, here are a couple of worksheets to accompany the homework.

Week 1 Review Worksheet and Trigonometry 1

Here are the slides of my presentation on Thursday July 30 — Lecture 4 Graphing Trig Relatations

Here is the first practice sheet on the material discussed in Lecture 4 Worksheet on graphing and trig equations 1

Here is another practice sheet that goes a bit further with the ideas we introduced on Thursday, but have not yet fully addressed in class. graphing and equations 2 challenge problems

 

Week 3


This week we will focus on more techniques of graphical representation of trigonometric functions. We will also explore the inverse trigonometric functions and properties of their graphs.

Here are the slides I will use on the first meeting.

amplidtude period and reflection

horizontal and vertical translation

inverse functions

Here is the worksheet that accompanies today’s discussion and homework.

Transformations and Inverses Worksheet

Here is the midterm which will be due at the start of class on Tuesday, July 12, 2016.

TrigMT Test Sheet


Week 4


This week we began our study of a very important aspect of trigonometry — that of the trigonometric identities. Since the trigonometric functions are ratios, products and sums of trigonometric functions satisfy many identities. A few are listed below.

\cos^2 x + \sin^2 x = 1.

1 + \tan^2 x = sec^2 x.

\cot^2 x + 1 = \csc^2 x.

These identities are called the Pythagorean identities because they are all derived from the Pythagorean theorem for triangles

a^2 + b^2 = c^2.

When working with identities, we want to try to transform one side of the expression into the other. In class on Thursday we demonstrated how to do that when we established the identity below:

\displaystyle{ \frac{\sin x}{1-\cos x}=\frac{1 +\cos x}{\sin x}} .

Here is another worksheet to get practice proving identities. The solutions are included for most of them in addition to the answers. Trigonometric Identities II

Next week we will continue with our study of identities in trigonometry by establishing the angle addition results.


Week 5


Tuesday we introduced the angle addition formulas for the sine and cosine functions. Here are some practice exercises to help you develop your skills at using these formulas. We also introduced the double angle and half angle formulas. Practice using these concepts is provided here as well.

Angle Addtion and Product Identitiestst More on Product and Sum Identities


Week 6


This week we will complete our study of algebraic identities involving trigonometric functions by concluding the discussion of the product to sum and sum to product formulas. We will then begin a study of how trigonometric functions can be used to represent complex numbers, thus bridging the gap between the real and complex number system. We will conclude this week with a study of triangles using the law of sines and cosines.

Homework for Thursday will be the above worksheet on “More on Product and Sum Identities” in addition to this worksheet which reviews complex numbers Complex Numbers Review.

The next worksheet is posted below for your convenience. It will cover calculating with trigonometric representations of complex numbers.

Complex Numbers and Trigonometry


Final Homework Project

Here is the final homework project which will be due at the start of class on Tuesday.

Final Homework Project Worksheet