# Homework 6

Due Thursday, May 4.

The following problems must be turned in (but will not be graded for correctness):

1. Make a table of values for tan, sec, csc, and cot, from 0 to 2pi. Note: some of these may be undefined.
2. Graph y = tan x from -2pi to 2pi. What is the period of tan?
3. Suppose $\mathrm{sin}(\theta) = \sqrt{3}/2$. Find $\mathrm{tan}(\theta)$ if $\theta$ is in quadrant I.

The following problems will be graded and will account for 30% of the homework’s grade:

1. A gardener has 200 feet of fencing with which to put around a rectangular garden. Find a function modeling the area of a garden he can make as a function of its width, if he wishes to use all 200 feet of fencing. Find the maximum of that function and use that to determine what would be the dimensions of the garden with the maximum area that he can make.
2. A bacteria culture initially weighs 2g and grows exponentially. 8 hours later, the culture weighs 18g. Find a function modeling the weight of the culture as a function of the time (in hours) since the initial observation. Use this function to determine when the bacteria will weigh 27g.
3. A (closed) rectangular box has a square base. Express its volume as a function of the base dimension x, if its surface area is 200 square feet.