Circles and Pythagorean identities

The  exercise appears under the Trigonometry Math Mission. This exercise connects the equation of a circle and the unit circle definition of trigonometric functions.

Types of Problems
There are three types of problems in this exercise:


 * 1) Find the abstract values: This problem provides a unit circle and some labels. The student is asked to find the values of different expressions in terms of the labeled variables.Capi1.png
 * 2) Select the answers about the circle: This problem provides a unit circle that is labeled with some specific values. The student is asked to select the correct answers to fill in the statements from drop-down menus.Capi2.png
 * 3) Find the exact value: This problem provides a specific trigonometric expression in a given quadrant. The student is expected to use this information to find a related trigonometric expression.Capi3.png

Strategies
Knowledge of conics and general trig identities are encouraged to ensure success on this exercise.
 * 1) One the unit circle the x-coordinate is the cosine of the angle of inclination and they y-coordinate is the sine value.
 * 2) On the Find the exact value problem the answers come out to be fractions, so knowing a handful of Pythagorean triples can help increase efficiency.
 * 3) Be careful to acknowledge the quadrant on this exercise, it will affect the sign of the trigonometric values.

Real-life Applications

 * 1) The Pythagorean trigonometric identities appear in calculus as a power simplification technique.
 * 2) The Pythagorean trigonometric identities appear on standardized tests like the SAT II.