Topographic surveying; including geographic, exploratory, and military mapping, with hints on camping, emergency surgery, and photography . 68.—TrigonometricFunctions. 257. Fundamental Formulas for Trigonometric Func-tions The fundamental formulas are : sin a -j- cos a z=. \; cos a sec « 1= I ; sin a I -|- tan a = tan aI cos a COS asec o tan a cot « = i ;sin « cosec a =cot or =I I ;cos a I -{- cot a = sin a sm «r= cosec a; versed sin a = i — cos 258. Formulas for Solution of Right-angled Tri-angles.—In the right-angled triangle, Fig. 168, 594 SOLUTION OF EIGHT-ANGLED TRIANGLES, 595 Let a = alt
Topographic surveying; including geographic, exploratory, and military mapping, with hints on camping, emergency surgery, and photography . 68.—TrigonometricFunctions. 257. Fundamental Formulas for Trigonometric Func-tions The fundamental formulas are : sin a -j- cos a z=. \; cos a sec « 1= I ; sin a I -|- tan a = tan aI cos a COS asec o tan a cot « = i ;sin « cosec a =cot or =I I ;cos a I -{- cot a = sin a sm «r= cosec a; versed sin a = i — cos 258. Formulas for Solution of Right-angled Tri-angles.—In the right-angled triangle, Fig. 168, 594 SOLUTION OF EIGHT-ANGLED TRIANGLES, 595 Let a = altitude,d = base, andc = hypothenuse ; and leta,/?, and ;/= the angles opposite a, b, and c, respectively;also letA = area of triangle, andR = radius of circumscribed circle. For a right-angled triangle y = 90° ; the fundamentalvalues of a, b, and A are then a — c s\vi a =L c cos ft = b tan a = b cotan ft;b = c sin ft = c cos a =^ a tan ft =. a cotan a; andA = ^ab = ^a cotan a = ^b^ tan a = ^c sin 2a. Fig. 169 furnishes a method of graphically stating theformulas relating to the solution of right-angled triangles. \ seAant. Fio. 169.—Graphic Statement of Formulas for Solution ofRight-angled Triangles. Let P = perpendicular in a right-angled triangle, theangle between the base of which, B, and the hypothenuse, //,is denoted by a. Then the diagram is applied by the use of the followingrules, the order of sequence being to follow either the names 596 SOLUJIOiV OF TRIANGLES. ?vvrittei around the circumference of the circle or by followingthe names along the intersecting lines in the order written;thus: I. Any trigonometric function or part equals the adjacentpart divided by the following part. Example: also,and sin a = cos a cot a sin a = a7 a c cos a 2. Any part equals the product of the adjacent : a = c sin ex = I? tan a; cosin a = sin a cotan a. 3. Each part equals the reciprocal of the opposite part Example: I I tan := —? ; sec a = cotan a cosin a 4.
Size: 1817px × 1376px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., book, bookcentury1900, bookdecade1900, bookpublishernewyorkjwiley
