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    Trigonometry Application Word Problems : Tan Function, Nautical Miles and Polar Coordinates of Nonagons

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    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 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 - zip code is 07018 or use another if necessary).
    (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 option 1 or option 2 or option 3 for polar coordinate graph paper.

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    Solution Preview

    1. (a) There's no value of the graph at x = 90.
    (b) x = 90, 270, etc ... i.e. x = 90 + 180k, where k is an integer.
    (c) For an angle close to 90 degrees and greater than 90 degrees, the tan is a very large negative number. For an angle close to 90 degrees ...

    Solution Summary

    This solution provides a step by step response which illustrates how to solve all three of these trigonometry based word problems. All calculations are provided.