# Simple Trig Identities

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```					Simple Trig Identities
Lesson 2.4b

Definition of An Identity
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Any equation that is true for every number in the domain of the equation. Example
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2x + 12 = 2(x + 6) Ratio Identities Reciprocal identities Pythagorean identities

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Trig identities
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Ratio Identities
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Since we know that x = cos t and y = sin t

…

y sin t tan t   x cos t x cos t cot t   y sin t
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Reciprocal Identities
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Identities given by definition

1 sin t  csc t

1 cos t  sec t

1 cot t  tan t

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Pythagorean Identities
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Consider that x2 + y2 = 1 Thus

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sin t  cos t  1
2 2

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Similarly

1  tan t  sec t
2 2

1  cot t  csc t
2 2

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Working with Identities
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Simplifying expressions using identities Given cot t  sin t
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Simplify

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Give a justification for each step

cot t  sin t cos t  sin t sin t cos t

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Working with Identities
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Tips
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sin 2 t  cos 2 t  1  cos 2 t  1  sin 2 t

In an expression, look for a part of the expression that looks like part of one of the identities Substitute that in Look for factors to cancel Look for terms of an expression that can be combined to form one of the identities Also possible to look at identities in different forms
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Practice
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Try these

csc t  cot t cot t

2

1  sin 2 t cot 2 t
Experiment with what your calculator does with these expressions

1 tan t  tan t

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Assignment
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Lesson 2.4b Page 167 Exercises 55 – 97 odd

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