. Elements of theoretical and descriptive astronomy, for the use of colleges and academies. 242 APPENDIX. APPENDIX. MATHEMATICAL DEFINITIONS AND FORMULA PLANE TRIGONOMETRY. 1. The complement of an angle or arc is the remainder obtained by subtracting the angle or arc from 90°. 2. The supplement of an angle or arc is the remainder obtained by subtracting the angle or arc from 180°. 3. The reciprocal of a quantity is the quotient arising from dividing 1 by that quantity: thus the reciprocal of a is -i~ 4. In the series of right triangles ABC, ABC, ABCt &c,C\ 1B ^ navmg a common angle A, we have
. Elements of theoretical and descriptive astronomy, for the use of colleges and academies. 242 APPENDIX. APPENDIX. MATHEMATICAL DEFINITIONS AND FORMULA PLANE TRIGONOMETRY. 1. The complement of an angle or arc is the remainder obtained by subtracting the angle or arc from 90°. 2. The supplement of an angle or arc is the remainder obtained by subtracting the angle or arc from 180°. 3. The reciprocal of a quantity is the quotient arising from dividing 1 by that quantity: thus the reciprocal of a is -i~ 4. In the series of right triangles ABC, ABC, ABCt &c,C\ 1B ^ navmg a common angle A, we have by Geometry, BC BC _ BCAB ~~ ABf — ABBC BC BC. AC ~ AC ~ ACAB AB AITAC~ AC ~ ACThe ratios of the sides to each other are there-Fig. 79. fore fae same in all right triangles having thesame acute angle: so that, if these ratios are known in any oneof these triangles, they will be known in all of them. Theseratios, being thus dependent only on the value of the angle,without any regard to the absolute lengths of the sides, havereceived special names, as follows:The sine of the angle is the quotient of the opposite side BC divided by the hypothenuse. Thus, sin A = -jg- The tangent of the angle is the quotient of the opposite sidedivided by the adjacent Thus, tan A = TRIGONOMETRY. 243 The secant of the angle is the quotient of the hypothenuse AB divided by the adjacent side. Thus, sec A = 5. The cosine, cotangent, and cosecant of the angle are respec-tively the sine, tangent, and secant of the complement of theangle. Now, in Fig. 79, the angle ABC is evidently the com-plement of the angle BA C. Hence we have, A t> AC. cos A =
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