Learning Resources
Lesson
In Mathematical Modeling, Book 2, you studied many trigonometric identities. Reciprocal, Pythagorean, and quotient trigonometric identities were studied in great detail.
The game you will play in this Focus provides the opportunity to review previously learned trigonometric identities, and to learn new ones. Playing the game should reinforce understanding of the identity relationships and reintroduce equivalent forms of expressions.
To play the game, you must have an understanding of the trigonometric identities. The basic identities are given on page 246. Take time to review these formulas. You should recall, however, that each Pythagorean Identity can be rearranged in various forms.
Some helpful strategies for solving trigonometric identities are provided. You may want to view them before beginning the task assigned below.
To reinforce your understanding, prove each trigonometric identity below. Carefully record each proof in your exercise. Remember: When you are asked to prove that an equation is an identity, always identify all restrictions on the domain of the variables. As well, it is wise to record the strategies you use to prove each identity.
This focus centres around a game called Trident Fish. You can play the game as outlined in the text, or you may play a variation of it on the computer. The computer version is in the form of a memory game.
To play the game in the text:
- Get a copy of Blackline Master 4.4.1, on pages 441 to 444 of the Teacher's Resource Book, from your on-site teacher. Photocopy each of the four pages and cut out the cards. Return the Blackline Master sheets to your teacher.
- The rules of "Trident Fish" are outlined on page 245 of your text. It is similar to the card game "Go Fish," and should be played in groups of two or four.
- Carefully read the rules of the game and begin to play.
To play the computer version of the game:
- It might be helpful to obtain the Blackline Master mentioned above and familiarize yourself with the cards, as the same ones are used in the computer game.
- The object of this game is to reveal as many matching pairs as possible. When two cards are selected, if no match is made, they will be replaced face down. If a match is made, the pair will remain face up.
- To select a card, simply click on it. The computer will indicate whether or not a match is made.
- Two things are essential for success in this game: A good memory and a good knowledge of equivalent trigonometric expressions. When a card is selected you must remember where to find its match, if in fact it was earlier revealed.
Notebook Entry: Record strategies for proving trigonometric identities.
Note: You will need graph paper for the Investigation in the next lesson. Be sure to have some on hand.
Some additional examples are provided below.
Activity
C.Y.U. page 247 #1
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
Test Yourself
Prove each trigonometric identity below. Be sure to identify any restrictions on the domain of the variable.
Solutions
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