Symmetry and periodicity of trigonometric functions

The  exercise appears under the Trigonometry Math Mission. This exercise increases comfort with the period and even/odd identities in trigonometry.

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


 * 1) Write an equivalent expression: This problem provides an expression. The student is expected to write an equivalent expression using period or even/odd identities.Sapotf1.png
 * 2) Select the correct classifications: This problem provides various trigonometric expressions. The student is expected to classify each expression as equal, opposite or neither, or some other type of classification.Sapotf2.png
 * 3) Find equivalent expressions: This problem provides a trigonometric expression. The student is asked to select all of the options from a multiple select list that evaluate to the same value.Sapotf3.png

Strategies
Knowledge of as many trigonometric identities as possible will increase the likelihood of success on this exercise.
 * 1) The period of sine, cosine, secant and cosecant are all $$2\pi$$.
 * 2) The period of tangent and cotangent are $$\pi$$.
 * 3) The picture can be used to help answer these problems if one recognizes that the sine is the y-value and the cosine is the x-value on the unit circle.

Real-life Applications

 * 1) Recognizing and using identities is important for most sophisticated trigonometric applications.
 * 2) Trigonometry was used to find heights of mountains, such as Mount Everest, before the advent of satellites.