Trigonometric+Identities

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**Nick Houriet Chelsea Rugel Sarah Murray

TABLE OF CONTENTS ** Introduction: -Summary of unit -Unit objectives -History of Identities Podcast -GLOSSARY

PAGE 1 5.1 Using Fundamental Identities -List of Fundamental trigonometric identities -Voki -Fundamental trig identities document -Practice problems PowerPoint -Interactive a nd helpful sites -Ima ges

PAGE 2 5.2 Verifying Trigonometric Identities -Strategies for verifying trigonometric identities PowerPoint -Voki -Practice Problems/answer key 5.3 Solving Trigonometric Equations <span style="background-color: rgb(0, 255, 255); font-family: Calibri;">-steps to solving trigonometric equations -Solving trigonometric equations video -Solving trigonometric equations photostory -Useful sites -Practice problems/ answer key -Practice Quiz <span style="background-color: rgb(0, 255, 36);">-WORKS CITED <span style="display: block; font-size: 110%; font-family: 'Comic Sans MS',cursive; text-align: left;">

Trigonometric Identities are primarily used to help simplify and evaluate trigonometric functions. This section covers fundamental identities, verifying identities, and solving equations with identities. The 5 types of fundamental identities are used solve trigonometric functions, or to simplify trigonometric expressions. The main identities that recur are reciprocal identities, quotient identities, and Pythagorean identities. The methods for verifying identities are used to prove that they are identities, and to simplify them. Finally, you will learn the methods to use trigonometric identities to solve equations. Trigonometric Identities can be applied to solve situations involving measuring trajectories and triangles.
 * <span style="display: block; font-size: 120%; font-family: 'Trebuchet MS',Helvetica,sans-serif; text-align: center;">Unit Summary **



<span style="text-align: left; display: block; font-family: 'Comic Sans MS',cursive; font-size: 121%;"> 1. Develop trigonometric identities a. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Reciprocal, Quotient, Pythagorean, Cofuntion, and Even/odd Identities
 * <span style="display: block; font-size: 121%; font-family: 'Trebuchet MS',Helvetica,sans-serif; text-align: left;">Unit Objective **<span style="line-height: 115%; font-size: 28pt; font-family: Georgia,serif; text-align: right; display: block;"> <span style="display: block; font-size: 121%; font-family: 'Trebuchet MS',Helvetica,sans-serif; text-align: left;">

2. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Evaluate trigonometric functions a. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Learn the Fundamental Trigonometric identities b. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Use identities to evaluate functions <span style="text-align: left; display: block; font-family: 'Comic Sans MS',cursive; font-size: 121%;"> 3. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Simplify trigonometric functions a. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Factoring trigonometric expressions b. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Adding trigonometric expressions c. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Rewriting trigonometric expressions d. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Verifying trigonometric Identities

4. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Solve trigonometric equations <span style="display: block; text-align: left; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">a. Applying algebraic methods to solving trigonometric identities <span style="display: block; font-size: 110%; font-family: Tahoma,Geneva,sans-serif; text-align: left;"> b. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Solve quadratic type trigonometric identities <span style="text-align: left; display: block; font-family: 'Comic Sans MS',cursive; font-size: 121%;">c.<span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Solve equations with multiple angled. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> Use inverse functions to solve trigonometric equations d. Use inverse functions to solve trigonometric identities <span style="line-height: 115%; font-size: 120%; font-family: Georgia,serif;"> A podcast of the history of Trig Identities, and their creator. media type="file" key="Podcast trig identities.mp3"

[|GLOSSARY OF TERMS.doc]

<span style="font-size: 28pt; line-height: 115%; font-family: 'Georgia','serif';">5.1 Using Fundamental Identities <span style="font-family: 'Footlight MT Light','serif'; position: relative; top: 5pt;"> <span style="display: block; font-size: 14pt; line-height: 115%; font-family: Georgia,serif; text-align: center;">
 * <span style="display: block; font-size: 14pt; line-height: 115%; font-family: Georgia,serif; text-align: center;">Fundamental Trigonometric Identities **<span style="line-height: 115%; font-size: 28pt; font-family: Georgia,serif; text-align: right; display: block;">

<span style="display: block; font-size: 14pt; line-height: 115%; font-family: Georgia,serif; text-align: left;"> <span style="display: block; font-size: 14pt; line-height: 115%; font-family: Georgia,serif; text-align: center;">

<span style="line-height: 115%; font-size: 28pt; font-family: Georgia,serif; text-align: right; display: block;">media type="custom" key="3958145" <span style="font-size: 28pt; line-height: 115%; font-family: 'Georgia','serif';">

Click to view step by step examples that coordinate with the lesson.

Click to view a powerpoint with extra 5.1 practice problems.

Click [|here] to visit an interactive problems site. Attempt to solve problems 1-6 to better understand the unit. . Click [|here] to link to a site that allows you to simplify problems step by step and gives you advice along the way.

Click [|here] for a simple review game of the lesson.

Click [|here] for a useful interactive trigonometry glossary