Plane And Spherical Trigonometry

Cover Plane And Spherical Trigonometry
Plane And Spherical Trigonometry
George N George Neander Bauer
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Draw the ordi- nate and abscissa of the point P. About as the center construct a circle with OP as a radius. Draw the tangents to this circle at L and F, the beginning of the first and second quadrants respectively, and produce them to intersect the terminal line, or the terminal line produced, in M and G.
Then y AP AP sin = - = = OP AP x OA OA KA cos a = - = = = OA r OP 1 x OA OL = x = OA = FG ==FG OP x OA OL FUNDAMENTAL RELATIONS 55 or Thus the trigonometric functions are represented by the s
...egments AP, OA, LM, FG, OM and OG. It is evident that these segments represent the trigonometric functions in magnitude. They also represent the trigonometric func- tions in sign. In accordance with the conventions of Arts. 6 and 11, the segments AP and LM are positive when drawn upward from the X-axis and negative when drawn down- ward ; the segments OA and FG are positive when drawn from the F-axis to the right and negative when drawn to the left; the segments OM and OG are positive when they coincide with the terminal line of the angle and negative when they coincide with the terminal line produced.

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