Khan Academy on a Stick : Basic Trigonometry

Khan Academy on a Stick

Trigonometry and precalculus

Basic trigonometry
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Introduction to trigonometry
Example: Using soh cah toa
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Worked example evaluating sine and cosine using soh cah toa definition.
Basic trigonometry II
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A few more examples using SOH CAH TOA
Secant (sec), cosecant (csc) and cotangent (cot) example
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Worked example where we walk through finding the major trig ratios
Example: Using trig to solve for missing information
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Worked example using trig ratios to solve for missing information and evaluate other trig ratios
Example: Calculator to evaluate a trig function
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Worked example showing how to use typical calculators to evaluate trigonometric functions
Example: Trig to solve the sides and angles of a right triangle
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Worked example using trigonometry to solve for the lengths of the sides of a right triangle given one of the non-right angles.
Example: Solving a 30-60-90 triangle
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This worked example can be done without trigonometry, but we do show how knowledge of 30-60-90 triangles can be helpful when evaluating trig functions
Using Trig Functions
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Using Trigonometric functions to solve the sides of a right triangle
Using Trig Functions Part II
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A couple of more examples of using Trig functions to solve the sides of a triangle.

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.

Introduction to radians
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Understanding the definition and motivation for radians and the relationship between radians and degrees
Radian and degree conversion practice
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A little practice converting between radians and degrees and vice versa
Example: Radian measure and arc length
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Worked example that thinks about the relationship between an arc length and the angle that is subtended by the arc.
Example: Converting degrees to radians
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Worked example to help understand how we covert radians to degrees
Example: Converting radians to degrees
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Worked example showing how to convert radians to degrees
Radians and degrees
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What a radian is. Converting radians to degrees and vice versa.

Radians

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 trig functions
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Extending SOH CAH TOA so that we can define trig functions for a broader class of angles
Example: Unit circle definition of sin and cos
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Unit circle definition to calculate sin and cos of multiple angles
Example: Using the unit circle definition of trig functions
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Worked example using our knowledge of 30-60-90 triangles and similarity to evaluate tan, cos and sin.
Example: Trig function values using unit circle definition
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Worked example that uses the unit circle definition to evaluate trig functions
Example: The signs of sine and cosecant
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Using the unit circle definition to think out the sin and cosine of a negative angle.

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.

Example: Graph, domain, and range of sine function
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Graphing a sin curve to think about its domain and range.
Example: Graph of cosine
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Basic interpretation of the graph of the cosine function
Example: Intersection of sine and cosine
Thinking about where the graphs of sin and cos intersect.
Example: Amplitude and period
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Determining the amplitude and period of a trig function
Example: Amplitude and period transformations
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Understanding how the amplitude and period changes as coefficients change.
Example: Amplitude and period cosine transformations
Visualizing changes in amplitude and period for a cosine function
Example: Figure out the trig function
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Determining a trig function given its graph
Graph of the sine function
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Using the unit circle definition of the sine function to make a graph of it.
Graphs of trig functions
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Exploring the graphs of trig functions
Graphing trig functions
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Analyzing the amplitude and periods of the sine and cosine functions.
More trig graphs
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Determining the equations of trig functions by inspecting their graphs.
Determining the equation of a trigonometric function
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Determining the amplitude and period of sine and cosine functions.

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: Arcsin
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Introduction to the inverse trig function arcsin
Inverse Trig Functions: Arccos
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Understanding the inverse cosine or arccos function
Inverse Trig Functions: Arctan
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Understanding the arctan or inverse tangent function.
Example: Calculator to evaluate inverse trig function
Example using calculator to evaluate inverse tangent function

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
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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!