3 5 derivatives of trig functions
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3.5 DERIVATIVES OF TRIG FUNCTIONS PowerPoint PPT Presentation


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3.5 DERIVATIVES OF TRIG FUNCTIONS. Some needed trig identities:. Trig Derivatives. Graph y 1 = sin x and y 2 = nderiv (sin x) What do you notice?. Proof Algebraically. (use trig identity for sin(x + h) ). Proof Algebraically. 0. 1. Trig Derivatives.

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3.5 DERIVATIVES OF TRIG FUNCTIONS

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3 5 derivatives of trig functions

3.5 DERIVATIVES OF TRIG FUNCTIONS


Some needed trig identities

Some needed trig identities:


Trig derivatives

Trig Derivatives

  • Graph y1 = sin xand y2 = nderiv (sin x)

    • What do you notice?


Proof algebraically

Proof Algebraically

(use trig identity for sin(x + h))


Proof algebraically1

Proof Algebraically

0

1


Trig derivatives1

Trig Derivatives

  • Graph y1 = cos xand y2 = nderiv (cos x)

    • What do you notice?


Proof algebraically2

Proof Algebraically

(use trig identity for cos(x + h))


Proof algebraically3

Proof Algebraically

0

1


Other trig derivatives

Other Trig Derivatives

(quotient rule)

(trig id cos2x + sin2x = 1)


Other trig derivatives1

Other Trig Derivatives

(quotient rule)


Other trig derivatives2

Other Trig Derivatives

(quotient rule)


Other trig derivatives3

Other Trig Derivatives

(quotient rule)


Example

Example

  • Find an equation of the tangent line to the function

    f(x) = sec x at the point

(slope)


Example1

Example

  • Find the second derivative of y = csc x.

(Product rule)


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