Chapter 5.1

5.1 Using Fundamental Identities In this chapter, you will learn how to use the fundamental identities to do the following: Evaluate trigonometric functions Simplify trigonometric expressions Develop additional trigonometric identities Solve trigonometric equations

5.1 Using Fundamental Identities Using Identities to evaluate a function Why should you learn this? In calculus you will use trigonometric identities to simplify an expression. Ex: Homework p.347 #97 is an example

5.1 Using Fundamental Identities Quadrant II Quadrant IVQuadrant III Quadrant I

5.1 Using Fundamental Identities Using Identities to Evaluate a Function Given: Find: The value of all six trigonometric functions *Remember: Once you know the value of Sine and Cosine you can find the values of all six trigonometric functions

5.1 Using Fundamental Identities Given: *Use the information given to decide which quadrant Which quadrant are we in? 1 ______ Find: The value of all six trigonometric functions Looking at page 340 in your book: Can you see which identity we should use to find the value of sine?

5.1 Using Fundamental Identities Pythagorean Identity 2

5.1 Using Fundamental Identities Now we know 3 :

5.1 Using Fundamental Identities Now try #11 pg.345 4

5.1 Using Fundamental Identities Simplifying a Trigonometric Expression 5 Factor out a Use the distributive property Use the Pythagorean Identity Multiply

5.1 Using Fundamental Identities Verifying a Trigonometric Identity 7

5.1 Using Fundamental Identities Now try #45 pg To check graphically, use radian mode graph one side of the equation as and the other side of the equation as. (Select line style for and path style for. )

5.1 Using Fundamental Identities Factoring Trigonometric Expressions 9 a.) b.)

5.1 Using Fundamental Identities Now try #51 pg

5.1 Using Fundamental Identities *NOTE: On occasion, factoring or simplifying can best be done by rewriting the expression in terms of just one trigonometric function or in terms of sine or cosine alone. Simplify 11 :

5.1 Using Fundamental Identities Now try #67 pg

5.1 Using Fundamental Identities Enriched Pre-Calculus Rewriting a Trigonometric Equation Rewrite 13 so that it is not in fractional form.

5.1 Using Fundamental Identities Now try #69 pg

5.1 Using Fundamental Identities Enriched Pre-Calculus Trigonometric Substitutions 15 Use the substitution to write as a trigonometric function of.

5.1 Using Fundamental Identities Now try #81 pg

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