Plane Trigonometry, for Colleges and Secondary SchoolsLongmans, Green, and Company, 1899 - 206 páginas |
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Página 5
... greater than 1 , the characteristic is positive and is one less than the number of digits to the left of the decimal point ; when the number is less than 1 , the characteristic is negative , and is one more than the number of zeros ...
... greater than 1 , the characteristic is positive and is one less than the number of digits to the left of the decimal point ; when the number is less than 1 , the characteristic is negative , and is one more than the number of zeros ...
Página 12
... greater the number of places of decimals , the more nearly will the calculated values represent the true values of the numbers . In other words , the values of incommensurable num- bers can be found approximately ; and the degree of ...
... greater the number of places of decimals , the more nearly will the calculated values represent the true values of the numbers . In other words , the values of incommensurable num- bers can be found approximately ; and the degree of ...
Página 13
... greater than 5 or 5 followed by numbers ; thus , e.g. , 3.72 for 3.724 , 3.73 for 3.7261 and * This ratio and facts ( c ) are considered in Note C , Appendix . The read- ing only requires a knowledge of elementary geometry . † This ...
... greater than 5 or 5 followed by numbers ; thus , e.g. , 3.72 for 3.724 , 3.73 for 3.7261 and * This ratio and facts ( c ) are considered in Note C , Appendix . The read- ing only requires a knowledge of elementary geometry . † This ...
Página 18
... 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 in order to ...
... 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 in order to ...
Página 39
... greater than the sum of the lengths of the other two . One more instance : let two given angles be 85 ° and 105 ° and the included side be 40 inches ; this triangle is im- possible , since the sum of the two given angles is greater than ...
... greater than the sum of the lengths of the other two . One more instance : let two given angles be 85 ° and 105 ° and the included side be 40 inches ; this triangle is im- possible , since the sum of the two given angles is greater than ...
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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'.