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

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