From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!

# Trigonometric Functions Exercises

### Example 1

What is the largest the slope of f(x) = sin(x) ever gets? The smallest?

### Example 2

What is the largest the slope of f(x) = cos(x) ever gets? The smallest?

### Example 3

Let f(x) = -sin(x). Based on the discussion in this section, what is a reasonable formula for f ' (x)?

### Example 4

Let f(x) = -cos(x). Based on the discussion in this section, what is a reasonable formula for f ' (x)?

### Example 5

Find the derivative of the function. Be sure to use correct notation.

• f(x) = sin(x)

### Example 6

Find the derivative of the function. Be sure to use correct notation.

• g(z) = cos(z)

### Example 7

Find the derivative of the function. Be sure to use correct notation.

• h(y) = -sin(y)

### Example 8

Find the derivative of the function. Be sure to use correct notation.

• r(k) = -cos(k)