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!
All content in “Unit circle definition of trig functions”
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 radians
- Rotation by radians and quadrants
- Arc length as fraction of circumference
- Radians on the unit circle
- Finding arc length from radian angle measure
- Ratio between concentric arcs
- Example: Radian measure and arc length
- Radians and arc length
- Example: Converting degrees to radians
- Example: Converting radians to degrees
- Radian and degree conversion practice
- Degrees to radians
- Radians and degrees
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
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).
- Inverse trig functions: arcsin
- Inverse trig functions: arccos
- Inverse trig functions: arctan
- Example: Calculator to evaluate inverse trig function
- Evaluating inverse trig functions
- Solution set to sin equation
- Restricting domain of trig function to make invertible
- Inverse tan domain and range
- Inverse tangent scenario
- Understanding inverse trig functions
- Angle of sun with the ground based on shadow
- Modeling annual temperature variation with trigonometry
- Applying inverse trig function with model
- Inverse trig word problems