# 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

### Trig Derivatives

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

• What do you notice?

### Proof Algebraically

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

0

1

### Trig Derivatives

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

• What do you notice?

### Proof Algebraically

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

0

1

### Other Trig Derivatives

(quotient rule)

(trig id cos2x + sin2x = 1)

(quotient rule)

(quotient rule)

(quotient rule)

### Example

• Find an equation of the tangent line to the function

f(x) = sec x at the point

(slope)

### Example

• Find the second derivative of y = csc x.

(Product rule)