Problem Set

1. Consider the graph of y = tan x.

(a) How does it show that the tangent of 90 degrees is undefined?

(b) What are other undefined x values?

(c) What is the value of the tangent of angles that are close to 90
degrees (say 89.9 degrees and 90.01 degrees)?

(d) How does the graph show this?

2. A nautical mile depends on latitude. It is defined as length of a
minute of arc of the earth's radius. The formula is N(P) = 6066 - 31 cos
2P, where P is the latitude in degrees.

(a) Using the Cybrary and other course resources, find the exact
latitude (to 4 decimal places) of where you live, used to live, work, or
used to work (include the zip code).

(b) Using the latitude found in part a and the formula N(P), find the
length of a nautical mile to the nearest foot at that location.

(c) Next, use the formula N(P) to find the latitude where the nautical
mile is 6051 feet.

(d) Name two cities in the Northern Hemisphere and two in the Southern
that are close to the latitude found in part c.

3. When graphed using polar coordinates, the center of a regular nonagon
is at the origin and one vertex is at (6, 0 degrees) or (6, 0 radians).
Find the polar coordinates of the other vertices in both degrees and
radians.

Click HYPERLINK
"http://www.mathematicshelpcentral.com/graph_paper.htm" \t "blank"
option 1 or HYPERLINK "http://www.richardmartino.com/math/polar.htm"
\t "blank" option 2 or HYPERLINK
"http://www.math-tutors.com/printshop-polar.html" \t "blank" option 3
for polar coordinate graph paper.