Thinking about graphing on a coordinate plane, slope and other analytic geometry.
Functions and their graphs
Revisiting what a function is and how we can define and visualize one.
Polynomial and rational functions
Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions.
Exponential and logarithmic functions
An look at exponential and logarithmic functions including many of their properties and graphs.
Trig identities and examples
Parametric equations and polar coordinates
An alternative to Cartesian coordinates.
A detailed look at shapes that are prevalent in science: conic sections
Systems of equations and inequalities
What happens when we have many variables but also many constraints.
Sequences, series and induction
An assortment of concepts in math that help us deal with sequences and proofs.
Probability and combinatorics
Basics of probability and combinatorics
Imaginary and complex numbers
Understanding i and the complex plane
Hyperbolic trig functions
Motivation and understanding of hyperbolic trig functions.
Preview of the calculus topic of limits
In this tutorial, you will learn all the trigonometry that you are likely to remember in ten years (assuming you are a lazy non-curious, non-lifelong learner). But even in that non-ideal world where you forgot everything else, you'll be able to do more than you might expect with the concentrated knowledge you are about to get.
- Basic trigonometry
- Example: Using soh cah toa
- Trigonometry 0.5
- Basic trigonometry II
- Trigonometry 1
- Trigonometry 1.5
- Example with trig functions and ratios
- Example relating trig function to side ratios
- Trigonometric functions and side ratios in right triangles
- Example: Trig to solve the sides and angles of a right triangle
- Trigonometry 2
Someone has taken the sine of an angle and got 0.85671 and they won't tell you what the angle is!!! You must know it! But how?!!! Inverse trig functions are here to save your day (they often go under the aliases arcsin, arccos, and arctan).
You are now familiar with the basic trig ratios. We'll now use them to solve a whole bunch of real-world problems. Seriously, trig shows up a lot in the real-world.
You're now familiar with sine, cosine and tangent. Now you'll see that mathematicians have also defined functions that are the reciprocal of those: cosecant, secant and cotangent.
Most people know that you can measure angles with degrees, but only exceptionally worldly people know that radians can be an exciting alternative. As you'll see, degrees are somewhat arbitrary (if we lived on a planet that took 600 days to orbit its star, we'd probably have 600 degrees in a full revolution). Radians are pure. Seriously, they are measuring the angle in terms of how long the arc that subtends them is (measured in radiuseseses). If that makes no sense, imagine measuring a bridge with car lengths. If that still doesn't make sense, watch this tutorial!
You're beginning to outgrow SOH CAH TOA. It breaks down for angles greater than or equal to 90. It breaks down for negative angles. Sometimes in life, breaking a bad relationship early is good for both parties. Lucky for you, you don't have to stay lonely for long. We're about to introduce you to a much more robust way to define trigonometric functions. Don't want to get too hopeful, but this might be a keeper.
- Unit circle definition of trig functions
- Example: Unit circle definition of sin and cos
- Example: Using the unit circle definition of trig functions
- Example: Trig function values using unit circle definition
- Example: The signs of sine and cosecant
- Unit circle manipulative
- Unit circle
- Example: Calculator to evaluate a trig function
The unit circle definition allows us to define sine and cosine over all real numbers. Doesn't that make you curious what the graphs might look like? Well this tutorial will scratch that itch (and maybe a few others). Have fun.
- Example: Graph, domain, and range of sine function
- Example: Graph of cosine
- Example: Intersection of sine and cosine
- Example: Amplitude and period
- Example: Amplitude and period transformations
- Example: Amplitude and period cosine transformations
- Example: Figure out the trig function
- Graphs of sine and cosine
- Graph of the sine function
- Graphs of trig functions
- Graphing trig functions
- More trig graphs
- Determining the equation of a trigonometric function
- Features of trigonometric functions
- Graphs of trigonometric functions
Pi (3.14159...) seems to get all of the attention in mathematics. On some level this is warranted. The ratio of the circumference of a circle to the diameter. Seems pretty pure. But what about the ratio of the circumference to the radius (which is two times pi and referred to as "tau")? Now that you know a bit of trigonometry, you'll discover in videos made by Sal and Vi that "tau" may be much more deserving of the throne!