The Complete Guide to Trigonometry

Name: The Complete Guide to Trigonometry
Rating: 4.5 (27 reviews)

Become a trigonometry master

Created byMike O

Last updated 10/2019

English

English [Auto],

What you'll learn

Understand the 6 main trigonometry functions
Solve challenging word problems using trigonometry
Understand the Laws of Sine and Cosine
Use the unit circle and inverse trig functions
Graph the primary trigonometry functions and their transformations
Prove difficult trigonometric identities
Find trigonometry values using double, half-angle, and sum and different identities
Solve challenging trigonometry equations using a range of algebraic techniques

Course content

4 sections • 79 lectures • 10h 36m total length

Welcome to the course!1:02
Triangles 101: What is trigonometry?5:29
The following document will be a good reference to have handy throughout the course: http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf
Set your calculator to degree mode1:08
Sine, Cosine, and Tangent4:35
Secant, cosecant, and cotangent3:20
Find all 6 trig functions, part 13:58
Draw a right triangle with opposite 4 and hypotenuse 5, use the Pythagorean theorem to find the missing side, then compute sine, cosine, tangent and their reciprocals: cosecant, secant, cotangent.
Find all 6 trig functions part 24:37
The one thing to memorize in trig: 30-45-60 table9:20
How to find missing sides in a triangle5:15
Identify whether sine, cosine, or tangent applies, then solve the resulting algebra to find missing triangle sides. Explore adjacent, opposite, and the hypotenuse with examples and multiple methods.
What is an inverse?6:52
How to find missing angles in a triangle3:48
How tall is the tallest basketball player ever?4:12
Using trig to save your cat stuck in a tree4:38
Apply trigonometry to solve a ladder problem by using sine with opposite 7 feet and hypotenuse 20 feet. Determine the ladder angle, about 20.5 degrees, to reach the cat safely.
CHALLENGE: Which mountain is this?10:45
Angles 101: The basics7:58
Master the basics of angles—vertex, initial and terminal sides, rays, lines, and line segments—in degrees, including right angles, straight angles, full circles, the four quadrants, and negative angles.
Coterminal angles3:50
What is a radian? (And how to convert radians to degrees)6:55
Circle arc length6:43
Compute arc length using circumference or the formula s = r theta with theta in radians, and apply it to 180 degrees and 90 degrees examples.
Sector area of a circle3:53
Apply the circle area formula to find sector areas, using radians and degrees to identify fractions of the circle, as shown with 7π/4 and 45° examples.
Trig functions in the coordinate plane5:09
Explore trig functions on coordinate plane by mapping sine to y over radius, cosine to x over radius, and tangent to y over x, linking to unit circle and slope.
All Students Take Calculus: Acronym to recall positive and negative values5:01
Find trig values in the coordinate plane6:10
Learn to find sine, cosine, tangent for a point in the coordinate plane using a 3-4-5 triangle, sohcahtoa, and quadrant signs in the third quadrant.
Finding trig functions for quadrantal angles4:40
Reference angles11:03
Finding exact trig values, part 110:42
Finding exact trig values, part 25:03
Finding exact trig values, part 39:26
How do you find the area of a triangle?3:47
Finding the area of a triangle2:07
What is the Law of Sines?3:33
Can you have 2 answers to the same problem?8:55
Law of Sines, part 17:17
Law of Sines, part 29:28
Law of Cosines, part 19:55
Apply the law of cosines to solve non-right triangles, choosing the appropriate formula for side-side-side or side-angle-side cases, and practice finding missing sides and angles.
Law of Cosines, part 26:58
Apply the law of cosines to a side-side-side triangle, identify the largest angle opposite the largest side, avoid sign mistakes, and solve for angles using inverse cosign.
Unit 1 Test C #1-14 Solutions13:07
Unit 1 Test C #15-17 Solutions9:55

What is the unit circle?14:20
Page 3 of this document has a unit circle shown: http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf
An easy way to memorize the unit circle11:22
Memorize the unit circle by filling in coordinates for 30, 45, and 60 degrees and their radian forms, and apply quadrant signs with sine and cosine.
How to graph sine and cosine10:54
See the attached document for a guide on graphing trig functions throughout this unit.
How to graph tangent6:53
How to graph transformations (simple)10:19
How to graph cosecant and cotangent11:25
Learn to graph cosecant and cotangent by graphing sine and tangent and taking reciprocals, noting asymptotes where sine equals zero and using five-point, period-based plotting.
How to graph transformations (harder)13:23
Explore how to graph transformed trig functions by adjusting amplitude, period, phase shift, and vertical translation, using a five-point method and a step-by-step example for sine and cosine.
Graphs of inverse trig functions11:21
Find exact values for inverse trig functions9:04
Find compositions using inverse trig11:13
How to write inverse trig expressions algebraically6:58
Learn to convert inverse trig expressions into algebraic forms by drawing a right triangle, applying TOA, and using the Pythagorean theorem to express the angle without trig functions.
Solving trig equations, part 111:18
Solving trig equations, part 25:56
Unit 2 Test C #1-11 SOLUTIONS17:51

What is an identity?2:52
Use the attached cheat sheet throughout this unit as a resource, together with page 2 of the following document: http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf
The Pythagorean identities (proved)5:13
Explore the pythagorean identities, prove sine squared plus cosine squared equals one, and derive tangent and cotangent identities from these relationships.
Find trig values using identities8:21
Simplify trig expressions using identities5:30
How to prove trig identities, part 18:09
Practice proving trig identities by applying strategies: start with the more complicated side, reveal known identities, use algebra, then meet in the middle; if stuck, convert to sines and cosines.
How to prove trig identities, part 29:36
How to prove trig identities, part 35:31
How to prove trig identities, part 46:47
Sum and difference identities, part 115:44
Sum and difference identities, part 24:29
Double angle identities11:55
Half angle identities, part 111:54
Half angle identities, part 211:58
Learn how to apply half-angle identities to find exact cosine and tangent values, determine signs by quadrant using reference angles and ASTC, and simplify with conjugates.
How to prove double angle identities6:09
Unit 3 Test C #1-6 SOLUTIONS21:10
Unit 3 Test C #7-12 SOLUTIONS24:10

Unit 4 Intro: The 3-step process for solving trig equations8:48
How to find solutions to trig equations9:28
Use the attached resource for help throughout this unit in solving trig functions, as well as the identities on page 2 of this document: http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf
Finding solutions, part 25:18
Solving trig equations using the GCF5:31
Solving trig equations by factoring trinomials4:55
Solving trig equations using Pythagorean identities and factoring5:41
Apply the pythegor ean identity sec^2 theta = tan^2 theta + 1 to factor the equation, producing sec theta = -2 or -1 and theta = 180°, 120°, 240°.
Solving trig equations by squaring both sides5:40
Solving trig equations using double angle identities4:50
Solving trig equations using half angle identities6:59
Unit 4 Test C #1-3 SOLUTIONS11:43
Unit 4 Test C #4-5 SOLUTIONS12:58
Unit 4 Test C #6 SOLUTION12:27

Requirements

Geometry
Algebra 2

Description

Is math a challenge for you? Then consider what Albert Einstein wrote to a 7th grade student asking for advice on her math classes: "Don't worry about your difficulties in mathematics. I can assure you that mine are still greater."

Math is challenging for everyone, even those who are great at it (it just doesn't feel hard for them until they reach a higher level. But it's still hard).

But anyone can learn to do math well provided they have someone available to give them a good explanation. Look no further than this course.

I'm a high school mathematics teacher, and this course is designed to help you master trigonometry. It's a no-fluff version of all the trig essentials you would learn in a complete trigonometry course in school, with clear and to-the-point explanations geared towards helping you master the basics in the shortest time possible.

No stone is left unturned to give you the most complete trigonometry course out there.

One of the most important factors in learning any skill, math included, is the guidance of a patient and experienced instructor who can clearly explain to you what you need to do. Here are some reactions from some of my students and their parents who have worked with me:

"He has certainly fostered a love for math in my daughter."--Parent
"Very clear and thorough. Our daughter enjoys his class and is excelling in the subject.”--Parent
"I think he is an awesome math teacher. He really enjoys math and always challenges us.”--Student
"One of my favorite teachers. His teaching method is understandable and very easy to comprehend."--Student
"Best math teacher I have ever had"--Student

Who this course is for:

Anyone who wants to master trigonometry
Students looking to prepare for the SAT and ACT
Those looking to brush up on forgotten math skills
Anyone who enjoys solving problems
Homeschool students or parents wanting to match their curriculum to a standard classroom curriculum
Students looking to remediate over the summer, or get ahead for next school year

The Complete Guide to Trigonometry

What you'll learn

Explore related topics

Course content

Trigonometry Intro37 lectures • 3hr 51min

Trig Graphs and Inverses14 lectures • 2hr 32min

Trigonometric Identities16 lectures • 2hr 39min

Solving trig equations using identities12 lectures • 1hr 34min

Requirements

Description

Who this course is for: