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Tangents, Nautical Miles and Polar Coordinates of a Nonagon

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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)?

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 option 1 or option 2 or option 3 for polar coordinate graph paper.

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Solution Preview

(a) As is evident from the graph, there is no fixed value of y = tan x when x = 900. This is because the graph tends to go to infinity at x = 900 and there exists a vertical asymptote.
(b) Other undefined x values are -900, 2700, etc.
(c) For values close to 900, the tan values are extremely high, close to infinity but finite, depending on the precision of the calculator.

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 ...

Solution Summary

Tangents, Nautical Miles and Polar Coordinates of a Nonagon are investigated

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