Trig Ident

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Basic Trigonometric Identities
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Identity

• An equation that is true for any variable
• Ex. 2x x x Ex. (x2 16) (x
  4)(x 4)
• In both cases, one side can be replaced with the
  other.
• When working with identities, very often we will
  be rewriting an expression in a different, but
  equivalent form. Sometimes the direction will be
  to simplify, or to find what the expression is
  equivalent to.

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Basic Trigonometric Identities

• Reciprocal Identities
• Quotient Identities
• Pythagorean Identities

sin2q 1 - cos2q
tan2q sec2q - 1
cot2q csc2q - 1
cos2q 1 - sin2q
sec2q - tan2q 1
csc2q - cot2q 1
In order to successful with these types of
problems, you will have to memorize these.
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Do you remember the Unit Circle?
Where did our pythagorean identities come from??

• What is the equation for the unit circle?

x2 y2 1

• What does x ? What does y ?
• (in terms of trig functions)

sin2? cos2? 1
Pythagorean Identity!
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Take the Pythagorean Identity and discover a new
one!

• Hint Try dividing everything by cos2?

sin2? cos2? 1 . cos2? cos2? cos2?

tan2? 1 sec2?
Quotient Identity
Reciprocal Identity
another Pythagorean Identity
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Take the Pythagorean Identity and discover a new
one!

• Hint Try dividing everything by sin2?

sin2? cos2? 1 . sin2? sin2?
sin2?
1 cot2? csc2?
Quotient Identity
Reciprocal Identity
a third Pythagorean Identity
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One way to use identities is to simplify
expressions involving trigonometric functions.
Often a good strategy for doing this is to write
all trig functions in terms of sines and cosines
and then simplify. Lets see an example of this
substitute using each identity
simplify
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Simplifying trig Identity
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Simplifying trig Identity
3 .
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Simplifying trig Identity
4.
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Simplify each expression.
5.
7.
6.
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Simplifying Trigonometric Expressions
Identities can be used to simplify trigonometric
expressions.
Simplify.
9)
8)
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tanxsinx cosx
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Use quotient identity
Simplify fraction with LCD
Simplify numerator
Use pythagorean identity
sec x
Use reciprocal identity
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