Plane Trigonometry, for Colleges and Secondary SchoolsLongmans, Green, and Company, 1899 - 206 páginas |
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Página 5
... shown , are : ( 1 ) The characteristic of a logarithm can be written on mere inspection ; ( 2 ) The position of the decimal point in a number affects the char- acteristic alone , the mantissa being always the same for the same sequence ...
... shown , are : ( 1 ) The characteristic of a logarithm can be written on mere inspection ; ( 2 ) The position of the decimal point in a number affects the char- acteristic alone , the mantissa being always the same for the same sequence ...
Página 16
... shown graphically by means of a specially marked line . Both the latter methods are illustrated , for instance , on the map of the Kingdom of Saxony in The Times Atlas : 5 0 Scale 1 : 870000 . 5 10 English Miles ( 69.16 = 1 ° ) FIG . 1 ...
... shown graphically by means of a specially marked line . Both the latter methods are illustrated , for instance , on the map of the Kingdom of Saxony in The Times Atlas : 5 0 Scale 1 : 870000 . 5 10 English Miles ( 69.16 = 1 ° ) FIG . 1 ...
Página 18
... shown to be greater or less than another . But geometry , with the excep- tion of a few cases , does not show by exactly how much the one angle is greater or less than the other . In order to show this , measurement is necessary ; and ...
... shown to be greater or less than another . But geometry , with the excep- tion of a few cases , does not show by exactly how much the one angle is greater or less than the other . In order to show this , measurement is necessary ; and ...
Página 21
... shown in Art . 13 that each of these ratios has the same value as in Fig . 2 , no matter where the point P is taken on either one of the lines bounding an angle which is equal to A. For the sake of convenience of reference , each one of ...
... shown in Art . 13 that each of these ratios has the same value as in Fig . 2 , no matter where the point P is taken on either one of the lines bounding an angle which is equal to A. For the sake of convenience of reference , each one of ...
Página 24
... shown to have the same tangent , secant , etc. * L1 R L A M1 M Ꭱ FIG . 4 . ( 2 ) Let RAL and RAL , be any two un- equal acute angles , placed , for convenience , so as to have a common vertex A and a common boundary line AR . From any ...
... shown to have the same tangent , secant , etc. * L1 R L A M1 M Ꭱ FIG . 4 . ( 2 ) Let RAL and RAL , be any two un- equal acute angles , placed , for convenience , so as to have a common vertex A and a common boundary line AR . From any ...
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Términos y frases comunes
A+B+C acute angle algebraic angle of elevation central angle CHAPTER circle circumscribing cologarithm column computation cos² cosec cotangent deduced denoted Derive draw equal equation EXAMPLES expression figures find log Find the angle Find the distance Find the height find the number formulas geometrical Given log graph Hence Hipparchus hypotenuse inverse trigonometric functions isosceles triangle law of sines length M₁ mantissa mantissa of log mathematics method negative NOTE number of degrees number of sides OP₁ perpendicular proj Prove radian measure radius regular polygon revolving right angles right-angled triangle sec² secant Show shown sin² sin³ sine and cosine Solve spherical trigonometry subtended tan-¹ tan² tangent terminal line theorems tower triangle ABC trigono trigonometric functions trigonometric ratios turning line whole number X₁
Pasajes populares
Página 100 - These formulas can be expressed in words : In any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides multiplied by the cosine of their included angle.
Página 54 - The area of a triangle is equal to one-half the product of the base by the altitude ; therefore, if a and b denote the legs of a right triangle, and F the area, F = \ ab.
Página 122 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Página 192 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.
Página vii - ... facility other French books. In the Dictionary at the end, is given the meaning of every- word contained in the book. The explanatory words are placed at the end of the book, instead of at the foot of the page; by this method learners will derive considerable benefit.
Página 83 - P'M' = sin a, OP' = cos a, AT'" = tan a, JBT" = cot a, OT" = sec a, OT'" = cosec a, without reference to their signs : hence, we have, as before, the following relations : sin (180° — a) = sin a, cos (180° — a) — — cos a, tan (180° — a) = — tan a, cot (180° — a) = — cot a, sec (180° — a) = — sec a, cosec (180 — a) = cosec a, By a similar process, we may discuss the remaining arcs b question.
Página 5 - The characteristic of the logarithm of a number greater than 1 is a positive integer or zero, and is one less than the number of digits to the left of the decimal point.
Página 189 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17° and 68° 25' respectively : what is its height ? [1836 feet.
Página 54 - Hence, the area of a triangle is equal to one-half the product of any two sides ' and the sine of their contained angle. EXAMPLES. 1. Find the area of the triangle in which two sides are 31 ft. and 23 ft. and their contained angle 67° 30'.