Applications of Trigonometry Word Problems : Tangent Function, Nautical Miles and Polar Coordinates of Nonagon Vertices

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). 39.4645 for zip code 25401 (http://www.zipinfo.com/search/zipcode.htm)

(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.

Solution Summary

Tangent Function, Nautical Miles and Polar Coordinates of Nonagon Vertices are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

As a group, work together to submit the answers to the following problems. Use the Small Group Discussion Board to divide tasks, discuss strategies for solving problems, and check each other's work. The finished product should be one combined document for the entire group, showing all calculations and graphical representations u

Latitude presents special mathematical considerations for cartographers. Latitude is the north-south location on the earth between the equator and the poles. Since the earth flattens slightly at the poles, a nautical mile varies with latitude. A nautical mile is given by N(e) = 6066 - 31 * cosine 2e. e represents the latitude in

1. The graph of a tangent function is given. Select the equation for the following graph:
y = tan , y = tan( x +π ), y = tan x, y = tan
2. Graph two periods of the given tangent function.
y = 2 tan 2x
3. Graph two periods of the given cosecant or secant function.
y = 3 sec x
4.

Please assist with the attached problem.
(a) Calculate the Laplacian of function u(x,y,z) = x^3 - 3xy^2 + z^2 in 3D Cartesian coordinates.
(b) Convert the formula for u into formula for u involving cylindrical polarcoordinates. Then compute the Laplacian using the cylindrical polar form. Show that your answer here is the same

1 A box with its base in the xy-plane has its four upper vertices on the surface with equation z=48-3x^2-4y^2. What is the maximum possible volume.
2 Find the differential dw for w =ysin(x+z)
3 Find the equation of the plane tangent to z=-sin((pi)yx^2) at the point P =(1,1,0)