Trigonometry 1 with The Math Sorcerer

Name: Trigonometry 1 with The Math Sorcerer
Rating: 4.9 (308 reviews)

Trigonometry Course with Assignments and Solutions

Created byThe Math Sorcerer

Last updated 5/2026

English

What you'll learn

The Basics of Angles
The Difference Between Positive and Negative Angles
Knowledge of the Key Terms Surrounding Angles, Including the Initial Side, Terminal Side, and Vertex of an Angle
Special Types of Angles Including Acute, Obtuse, Right, and Straight Angles
How to Find Supplementary Angles
How to Find Complementary Angles
The Definition of an Angle in Standard Position
The Definition of a Quadrantal Angle
What it Means for Two Angles to be Coterminal
How to Find the Coterminal Angle of Least Positive Measure given an Angle
Understand what a Radian Actually Is
How to Convert from Radians to Degrees
How to Convert from Degrees to Radians
Knowledge of the Most Common Angles
How to Find the Arc Length
How to Find the Area of a Sector
Knowledge of Linear and Angular Speed
The Definition of the Trigonometric Functions
How to Find the Six Trigonometric Function Values of an Angle Given a Point on the Terminal Side of the Angle
How to Determine if a Trig Function is Positive or Negative in Any Quadrant
How to Determine the Quadrant of an Angle Given the Signs of the Trig Functions
The Ranges of all Six Trig Functions and How to Solve Problems Involving the Range
The Pythagorean Identities and How to Prove Them
How to Solve Problems using the Pythagorean Identities
How to Find the Six Trig Function Values of an Angle Given the Equation of the Terminal Side of the Angle
How to Write Certain Trig Functions in Terms of Other Trig Functions using the Pythagorean Identities
The Wonderful Acronym SOH CAH TOA and How to Use it Effectively
A Useful Mnemonic for Memorizing the Trig Function Values
The Cofunction Identities and How to Use Them
The Definition of a Reference Angle and How to Find Them
The Unit Circle
How to Compute Trig Function Values using the Unit Circle
How to Compute Trig Function Values using the Reference Angle Method
How to Solve a Right Triangle
How to Solve Application Problems Involving the Angle of Elevation
How to Find the Amplitude, Period, Phase Shift, Vertical Shift, and Range of the Sine and Cosine Functions
How to Graph Any Sine Function
How to Graph Any Cosine Function
How to Graph the Tangent Function
How to Graph the Cotangent Function
How to Graph the Secant Function
How to Graph the Cosecant Function
How to Solve Application Problems Involving Harmonic Motion

Course content

12 sections • 95 lectures • 5h 54m total length

Basic Terminology and Degrees14:03
Example 12:07
Example 22:17
Example 31:31
Example 41:14
Example 51:13
Example 61:18
Introduction to Degrees, Minutes, and Seconds5:56
Convert angles between degrees, minutes, and seconds into decimal degrees, understanding that one minute equals 1/60 of a degree and one second equals 1/3600 of a degree, illustrated by examples.
Standard Position, Quadrantal Angles, and Coterminal Angles11:42
Standard Position, Quadrantal Angles, and Coterminal Angles (version 2)9:05
Coterminal Angle Example 11:39
Coterminal Angle Example 21:17
Compute the coterminal angle for 539 degrees by subtracting 360 degrees to obtain the least positive measure of 179 degrees, noting coterminal angles differ by multiples of 360 degrees.
Coterminal Angle Example 31:07
Compute the coterminal angle of least positive measure for -20 degrees by adding 360 degrees until the result lies between 0 and 360, yielding 340 degrees.
Introduction to Radians8:26
Learn how radians define angle measures by equating arc length to radius and convert between degrees and radians using pi over 180 and 180 over pi.
Example 10:45
Example 20:34
Example 30:33
Example 40:35
Example 51:46
Example 61:44
Example 70:43
Common Angles and Arc Length3:42
Explore common angles in trigonometry and learn arc length via s = r theta, with a 6 metre radius and a 2-radian angle yielding 12 metres.
Example0:58
Area of a Sector1:17
Compute the area of a sector using the formula A = 1/2 R^2 theta with theta in radians; for R = 17.2 m and theta = pi/3, the area is about 154.90 m^2.
Introduction to Linear and Angular Speed6:18

Definition of the Trigonometric Functions6:37
The Signs of Trigonometric Functions4:17
The Ranges of Trigonometric Functions3:08
The Pythagorean Identities8:18
Example 13:07
Example 22:45
Example 33:21
Compute r = sqrt((-12)^2+(-5)^2) = 13, then sin = -5/13, cos = -12/13, tan = 5/12, with csc = -13/5, sec = -13/12, cot = 12/5.
Example 42:55
Example 52:56
Example 64:30
Example 75:34
Example 84:22
Example 91:09
learn how to find secant theta when cosine theta is two thirds by using the reciprocal, yielding secant theta equals three over two.
Example 103:42
Example 113:55
Example 122:28
Derive cos theta in terms of sin theta from the identity cos^2 theta + sin^2 theta = 1, solving for cos theta and taking the positive root for acute angles.
Example 134:25

Right Triangle Definitions of Trigonometric Functions3:54
Define the trigonometric functions from a right triangle using adjacent, opposite, and hypotenuse. Use sine, cosine, and tangent and their reciprocals cosecant, secant, cotangent, via soh cah toa.
Memorization Trick for Trig Function Values3:51
The Cofunction Identities4:51
Learn cofunction identities for sine, cosine, secant, cosecant, tangent, and cotangent with theta in degrees and radians. Examples convert secant 39° to cosecant 51° and tan π/3 to cotangent π/6.
Example3:03
Introduction to Reference Angles6:34
Finding Reference Angles: 3 Examples3:42
Find reference angles by measuring the acute angle between the terminal side and the x axis. Use examples with 240, 340, and -110 degrees to identify the reference angle.
The Unit Circle4:46
The Unit Circle PDF0:01
Example 13:06
Example 25:02
Find the reference angle for four pi over three and calculate the trig values for pi over three. Use quadrant three signs to determine sine, cosine, tangent, and reciprocals.
Example 36:05
Example 43:44
Example 52:41
Example 62:15
Derive the trig function values for 45 degrees using a 45–45–90 triangle and sohcahtoa, revealing sine and cosine as 1/√2, tangent as 1, and reciprocals csc and sec as √2.
Example 72:44
Example 81:07
Example 91:10
Learn how to determine the cosine of three pi over two using the unit circle, noting the point has x = 0, so cosine equals zero.
Example 101:41
Example 111:08
Compute the cosine of pi via the unit circle, noting that cosine is the x-coordinate and pi corresponds to the point (-1, 0).
Example 121:06
Example 132:55
Example 142:25
Example 153:17
Example 162:31
Example 171:09
Example 181:04
Example 191:13
Example 201:06
Example 210:59
Compute the sign of pi/2 using the unit circle, noting that at pi/2 the point is (0,1) and sine equals 1.
Example 222:32
Example 231:16
Example 242:23
Apply a minimal memorization method to determine the sine sign of five pi over three using the reference angle pi over three and the unit circle, yielding a negative value.
Example 252:00
Use the reference angle pi over six to determine the sign of sine for seven pi over six. In quadrant three, sine is negative and equals one half.
Find the y-coordinate of the point on the Unit Circle2:47
solve for the y coordinate on the unit circle by substituting x = sqrt(3)/2 into x^2 + y^2 = 1, then find y = -1/2 in quadrant four.
Show that the Point Lies on the Unit Circle1:59

Requirements

Some basic algebra skills can be helpful.

Description

This is a course on Trigonometry. This courses covers roughly the first half of what is typically taught in a college level course on Trigonometry, hence the name, Trigonometry 1. It includes tons of videos, as well as a few assignments with solutions. This course starts from the very beginning and it assumes you know some basic algebra, although very little algebra is actually used throughout the course. There are a few instances where some algebra does come up, but those instances are explained carefully in the videos. This course is intended for beginners.

One of the most difficult parts of trigonometry is computing the trigonometric function values, and so this course places extra emphasis on that topic. Several examples of computing trig function values are given and I explain different ways to compute them.

Here are some suggestions for how to use this course.

Watch the videos at your own pace. As you watch the videos, take notes and try to work through the examples I do by yourself.
Work through the assignments if you want to, although this really not a requirement.
Have fun, and remember trigonometry is super useful for learning further math.

I hope this course helps someone. Remember to try to have fun and work at your own pace.

Good luck:)

Who this course is for:

Anyone who wants to learn Trigonometry.

Trigonometry 1 with The Math Sorcerer

What you'll learn

Explore related topics

Course content

Angles and Their Measures25 lectures • 1hr 22min

Assignment with Solutions1 lecture • 1min

Trigonometric Functions and Fundamental Identities17 lectures • 1hr 7min

Assignment with Solutions1 lecture • 1min

Right Triangles and Evaluating Trigonometric Functions35 lectures • 1hr 32min

Assignment with Solutions1 lecture • 1min

Applications of Right Triangles3 lectures • 12min

Graphs of the Sine and Cosine Functions2 lectures • 1hr 5min

Graphs of the Other Circular Functions4 lectures • 20min

Harmonic Motion2 lectures • 10min

Requirements

Description

Who this course is for: