The Unit circle trigonometry exercise appears under the Trigonometry Math Mission. This exercise continues working on the unit circle and realizing how it relates to trigonometric values of angles.
Types of Problems[]
There are two types of problems in this exercise:
- Select the lengths with the trig values: This problem has a diagram of the unit circle and several labeled segments. The student is expected to select the lengths that have a particular trigonometric value.
Select the lengths with the trig value
- Select the trig expressions with the requested value: This problem has a unit circle and a particular point labeled. The student is asked to select all of the trig expressions that evaluate to a particular coordinate of the point from the circle.
Select the trig expressions with the requested value
Strategies[]
Knowledge of the unit circle and some of the basic identities are encouraged to ensure success on this exercise.
- The cofunction identities can be useful in understanding similar-valued trig expressions.
- The cosine value is the x-coordinate of the point.
- The sine value is the y-coordinate of the point.
Real-life Applications[]
- The unit circle is like a "times table" for the trig values of bench mark angles.
- Almost all of trigonometry is embedded in the unit circle.
- Trigonometry has applications in physics for many different types of motion and acceleration.
- Trigonometry has many applications in astronomy, music, analysis of financial markets, and many more professions.