math 1330 4.4.pdf - Section 4.4 Trigonometric Expressions...

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1 Section 4.4 Trigonometric Expressions and Identities In this section, you’ll learn to simplify trig expressions using identities and using basic algebraic operations. You can add, subtract, multiply, divide and factor trig expressions, in much the same manner that you can with algebraic expressions. Examples: 2 2sin 3sin 5sin 6cos 10cos 4cos tan( ) tan( ) tan( ) x x x x x x x x x   Notation: 2 2 sin( ) sin( ) sin( ) sin ( ) x x x x 3 3 cos( ) cos ( ) x x Be careful: 2 2 sin ( ) sin( ) x x sin 2 sin( 2) x x
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2 Example 1 : Perform the following operation and simplify:  cos( ) 5 cos( ) 7
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3 Example 2: Factor: 2 sin sin 2 x x
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4 Example 3 : Factor: 2 sec 4sec 12
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5 RECALL: 2 2 ( )( ) a b a b a b Example 4 : Factor completely: 4 2 tan tan x x
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