Khan Academy on a Stick
Unit circle definition of trig functions
Let's now extend the domain of the trig function we love by exploring the unit circle definition of trig functions!
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Introduction to radians
Understanding the definition and motivation for radians and the relationship between radians and degrees
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Rotation by radians and quadrants
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Arc length as fraction of circumference
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Finding arc length from radian angle measure
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Ratio between concentric arcs
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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.
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Example: Converting degrees to radians
Worked example to help understand how we convert radians to degrees
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Example: Converting radians to degrees
Worked example showing how to convert radians to degrees
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Radian and degree conversion practice
A little practice converting between radians and degrees and vice versa
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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!
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Introduction to the unit circle
Extending SOH CAH TOA so that we can define trig functions for a broader class of angles
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Unit circle manipulative
Walk-through of the Khan Academy Unit Circle manipulative: http://www.khanacademy.org/math/trigonometry/e/unit_circle
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Matching ratios to trig functions
Trig problems on the unit circle
Solving triangle in unit circle
Finding trig functions of special angles exampleTrig 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.
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Inverse trig functions: arcsin
Introduction to the inverse trig function arcsin
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Inverse trig functions: arccos
Understanding the inverse cosine or arccos function
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Inverse trig functions: arctan
Understanding the arctan or inverse tangent function.
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Example: Calculator to evaluate inverse trig function
Example using calculator to evaluate inverse tangent function
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Solution set to sin equation
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Restricting domain of trig function to make invertible
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Inverse tan domain and range
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Inverse tangent scenario
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Angle of sun with the ground based on shadow
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Modeling annual temperature variation with trigonometry
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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).