5.1 Using Fundamental Identities

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Chapter 5.1
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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

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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

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5.1 Using Fundamental Identities
Quadrant II
Quadrant I
Quadrant IV
Quadrant III
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5.1 Using Fundamental Identities
Using Identities to Evaluate a Function Given F
ind 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
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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?
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5.1 Using Fundamental Identities
Pythagorean Identity2
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5.1 Using Fundamental Identities
Now we know3
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5.1 Using Fundamental Identities
Now try 11 pg.3454
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5.1 Using Fundamental Identities
Simplifying a Trigonometric Expression5
Factor out a Use the distributive property Use
the Pythagorean Identity Multiply
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5.1 Using Fundamental Identities
Verifying a Trigonometric Identity7
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5.1 Using Fundamental Identities
Now try 45 pg.3468
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 . )
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5.1 Using Fundamental Identities
Factoring Trigonometric Expressions9
a.) b.)
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5.1 Using Fundamental Identities
Now try 51 pg.34610
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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. Simplify11
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5.1 Using Fundamental Identities
Now try 67 pg.34612
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5.1 Using Fundamental Identities
Enriched Pre-Calculus Rewriting a Trigonometric
Equation
Rewrite13 so that it is not
in fractional form.
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5.1 Using Fundamental Identities
Now try 69 pg.34614
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5.1 Using Fundamental Identities
Enriched Pre-Calculus Trigonometric
Substitutions15
Use the substitution
to write as a trigonometric function
of .
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5.1 Using Fundamental Identities
Now try 81 pg.34716
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THE END