Khan Academy on a Stick

Basic trigonometric ratios

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.


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!

Unit circle definition of trigonometric functions

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.

Graphs of trig functions

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.

Inverse trig functions

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).

  • Tau versus Pi

    Why Tau might be a better number to look at than Pi

Long live Tau

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!