Chapter 3 Section 06

Chapter 3 Section 06 - 3.6 Derivatives of Trig Functions...

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1 3.6 Derivatives of Trig Functions page 167
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2 Objectives 1. Verify the derivative of sine using the definition of derivative. 2. Find the derivatives of the six trig functions. 3. Find equations of lines tangent to given trig graphs.
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3 Notation review: sin 2 (x) = [sin(x)] 2 sin x 2 = sin(x 2 ) [sin(x)] -1 = 1/sin(x) = csc(x) sin -1 (x) = arcsin(x)
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4 Trig Rules D x [sin(x)] = cos(x) D x [cos(x)] = -sin(x) D x [tan(x)] = sec 2 (x) D x [csc(x)] = -csc(x)cot(x) D x [sec(x)] = sec(x)tan(x) D x [cot(x)] = -csc 2 (x)
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5 Proof of D x [sin(x)] = cos(x) ) cos( 1 ) cos( 0 ) sin( ) sin( lim ) cos( 1 ) cos( lim ) sin( ) sin( ) cos( lim ) sin( ) cos( ) sin( lim ) sin( ) cos( ) sin( ) cos( ) sin( lim ) sin( ) cos( ) sin( ) cos( ) sin( lim ) sin( ) sin( ) cos( ) cos( ) sin( lim ) sin( ) sin( lim ) ( ' 0 0 0 0 0 0 0 0 x x x h h x h h x h h x h x h x h h x h x h x h h x x h x h x h x h x h x h x x f h h h h h h h h = + = + - = + - = + - = + - = - + = - + =
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6 ) ( sec ' ) ( cos ' ) ( cos ) ( sin
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This note was uploaded on 09/28/2009 for the course MATH 1550 taught by Professor Wei during the Spring '08 term at LSU.

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Chapter 3 Section 06 - 3.6 Derivatives of Trig Functions...

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