This document summarizes the derivatives of trigonometric functions. It states that the derivatives of sin(x) is cos(x) and the derivative of cos(x) is -sin(x). It then lists the derivatives of other trigonometric functions like tan(x), cot(x), sec(x), and csc(x). It notes that the derivatives of the "co-" functions are the negatives of the derivatives of their corresponding functions. The document also provides examples of using the product rule and quotient rule to take derivatives of trigonometric functions. It assigns problems from page 146 as homework.

1. Derivatives of Trigonometric Functions

2. If y = sin x, then y’ = cos x For example: If given y = 3x - 5 sinx and asked to find y’ y’ = 3 - 5 cos x

3. If y = cos x, then y’ = -sin x For example: If given y = 7x 2 + 2cos x and asked to find y’ you would get y’ = 14x - 2sinx

4. So you already know the derivatives of sin x and cos x. Here are the rest: y y’ sin x cos x cos x -sin x tan x sec 2 x cot x -csc 2 x sec x sec x tan x csc x -csc x cot x

5. HINTS: All the derivatives of the “co”-functions are negatives. They are also the opposite of whatever they are the co-function of. For example: The derivative of tan x is sec 2 x, so the derivative of the co-function of tan x, cot x, is negative and the opposite of sec x, so you get -csc 2 x.

6. Examples: y = 3 csc x y’ = -3 csc x cot x y = 5x 3 + tan x y’ = 15x 2 + sec 2 x

7. Product Rule and Quotient Rule still apply. y = x 2 sin x y’ = uv’ + vu’ y’ = x 2 cos x + sin x · 2x or y’ = x 2 cos x + 2x sin x

8. Do page 146 (1 - 10) for HW