The Tangent of 2X

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Authors
Rigge, William F., S.J.
Issue Date
1922-10
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Article
Language
en_US
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Rigge Papers , Mathematics
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Abstract
First Paragraph | The object of this article is to show an interesting and practical application of one of the well-known formulas of trigonometry that appear to be so dry and valueless to the student who must memorize them, and so purely theoretical and pedagogical to the instructor who exacts them. It is the formula tan 2x = 2 tanx/(I —tan2x). This can be used to find the focal length as well as the position of the camera in certain cycloramic pictures. The essential element of this picture must be a straight wall of some kind or its equivalent, or at the very least, certain five points that we need must be in a straight line, such as the points, A, B, P, E, D, in the diagram, and this line must be so placed that it will contain the foot of the perpendicular P dropped to it from the camera C. With this requirement we combine the fact that, as the camera lens revolves, equal fractional lengths of the film will correspond to equal horizontal angles in space, the exact proportion being unknown at the start. These two, the straight wall and the equiangular film, will solve the problem.
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