Plane Trigonometry, for Colleges and Secondary SchoolsLongmans, Green, and Company, 1899 - 206 páginas |
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Página 4
... shows that the logarithms of numbers between 1 and 10 lie between 0 and 1 , between 10 and 100 lie between 1 and 2 , between 100 and 1000 lie between 2 and 3 , and so on . ( 1 ) .... For example , 9 = 10-95424 , 247 = 102.39270 , 1453 ...
... shows that the logarithms of numbers between 1 and 10 lie between 0 and 1 , between 10 and 100 lie between 1 and 2 , between 100 and 1000 lie between 2 and 3 , and so on . ( 1 ) .... For example , 9 = 10-95424 , 247 = 102.39270 , 1453 ...
Página 6
Daniel Alexander Murray. This logarithm is usually written 3.40449 , in order to show that the minus sign affects the characteristic alone . In order to avoid the use of negative characteristics , 10 is often added to the loga- rithm and ...
Daniel Alexander Murray. This logarithm is usually written 3.40449 , in order to show that the minus sign affects the characteristic alone . In order to avoid the use of negative characteristics , 10 is often added to the loga- rithm and ...
Página 9
... shows some of its applications . The truths of elementary trigonometry are founded upon geom- etry , and are obtained and extended by the help of arithmetic and algebra . A knowledge of the principal facts of plane geome- try , and the ...
... shows some of its applications . The truths of elementary trigonometry are founded upon geom- etry , and are obtained and extended by the help of arithmetic and algebra . A knowledge of the principal facts of plane geome- try , and the ...
Página 18
... show by exactly how much the one angle is greater or less than the other . In order to show this , measurement is necessary ; and in order to measure , a unit angle of measurement must be chosen . The unit of angular magnitude which is ...
... show by exactly how much the one angle is greater or less than the other . In order to show this , measurement is necessary ; and in order to measure , a unit angle of measurement must be chosen . The unit of angular magnitude which is ...
Página 25
... in a counter - clock- wise direction , starting from the position AM : show that , as the angle MAL * These are usually called Logarithmic sines , tangents , etc. increases , its sine , tangent , and secant increase 13. ] 25 TABLES .
... in a counter - clock- wise direction , starting from the position AM : show that , as the angle MAL * These are usually called Logarithmic sines , tangents , etc. increases , its sine , tangent , and secant increase 13. ] 25 TABLES .
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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'.