. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . cosec 0 =I. tan (9 = 1 a 1 , sec# = sin 0sin 6 COS0 cot0 = tan 0 cos# For , * a c sin 6 tan 0 = - = - 6 c COS0 II. sin20 + cos2<9 = l. Forsin20 + cos20 = ^ + ^ = ^^ = c2 c2 III. sec2<9=l + tan2<9. For sec20=-: b2 + a2 b2 b2IV. cosec20=:l + cot20. ! + ^=l+tan*Ab1 For cosec2(9=-=^±^2=l+-=l+cot2ft. cot Formulae L, II., III., IV. are very important, and must beremembered. * a, by c are numbers, being the number of times the lengths of the sides containsome ch
. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . cosec 0 =I. tan (9 = 1 a 1 , sec# = sin 0sin 6 COS0 cot0 = tan 0 cos# For , * a c sin 6 tan 0 = - = - 6 c COS0 II. sin20 + cos2<9 = l. Forsin20 + cos20 = ^ + ^ = ^^ = c2 c2 III. sec2<9=l + tan2<9. For sec20=-: b2 + a2 b2 b2IV. cosec20=:l + cot20. ! + ^=l+tan*Ab1 For cosec2(9=-=^±^2=l+-=l+cot2ft. cot Formulae L, II., III., IV. are very important, and must beremembered. * a, by c are numbers, being the number of times the lengths of the sides containsome chosen unit of length. 30 PLANE TRIGONOMETRY. 24. Use of the Preceding Formulae. I. To express all the other functions in terms of the sine. Since sin2 0 + cos2 0 = 1, . \ cos 0 = ± V1 — sin2 0 sin 0 tan0 = cos 0 VI -sin2 0 ,.n 1 LVl-sin20 cot0 = - = ± ———- tan 0 sin 0 sec0 =cosec0 = cos (9 Vl-sin20 1 sin0 II. To express all the other functions in terms of the tan-gent. Since tan0 = ^, COS0 e- zj i^/)^/] tan0 . tan 0sin 0 = tan 0 cos 0 = = ± — COS0: sec0 Vl+tan20 1 1 sec0 Vl + tan201 cot0 = —— seed = ± Vl + tan* 0 a 1 , Vl + tan2<9 cosec 0 = ~—- = ± -—-— sin 0 tan 0 Similarly, any one of the functions of an angle may beexpressed in terms of any other function of that sign of the radical will in all cases depend upon thequadrant in which the angle 0 lies. 25. Graphic Method of fin
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Keywords: ., bookcentury1900, bookdecade1900, booksubjecttrigono, bookyear1902
