Unit circle definition of trig functions : Khan Academy on a Stick

Khan Academy on a Stick

Trigonometry

Basic trigonometry
Unit circle definition of trig functions
Graphs of trig functions
Trig identities and examples

Introduction to radians
Understanding the definition and motivation for radians and the relationship between radians and degrees
Rotation by radians and quadrants
Arc length as fraction of circumference
Finding arc length from radian angle measure
Ratio between concentric arcs
Example: Radian measure and arc length
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
Worked example to help understand how we convert radians to degrees
Example: Converting radians to degrees
Worked example showing how to convert radians to degrees
Radian and degree conversion practice
A little practice converting between radians and degrees and vice versa
Radians and degrees
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!

Introduction to the unit circle
Extending SOH CAH TOA so that we can define trig functions for a broader class of angles
Unit circle manipulative
Walk-through of the Khan Academy Unit Circle manipulative: http://www.khanacademy.org/math/trigonometry/e/unit_circle
Matching ratios to trig functions

Trig problems on the unit circle

Trig functions of special angles

In this tutorial, we'll really digest how special triangles and angles that show up a lot in mathematics relate to each other and the various trig functions.

Inverse trig functions: arcsin
Introduction to the inverse trig function arcsin
Inverse trig functions: arccos
Understanding the inverse cosine or arccos function
Inverse trig functions: arctan
Understanding the arctan or inverse tangent function.
Example: Calculator to evaluate inverse trig function
Example using calculator to evaluate inverse tangent function
Solution set to sin equation
Restricting domain of trig function to make invertible
Inverse tan domain and range
Inverse tangent scenario
Angle of sun with the ground based on shadow
Modeling annual temperature variation with trigonometry
Applying inverse trig function with model

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).