Plane Trigonometry, for Colleges and Secondary SchoolsLongmans, Green, and Company, 1899 - 206 páginas |
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Página 12
... four , in fact , to as many places of decimals as one please . The 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 ...
... four , in fact , to as many places of decimals as one please . The 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 ...
Página 15
... four times as great ? Compare , if possible , the angles in these triangles . 13. ( a ) In a right - angled triangle the hypotenuse is 35 yd . and the per- pendicular is 15 yd .; calculate the ratios specified in Ex . 8 , Art . 8 . ( b ) ...
... four times as great ? Compare , if possible , the angles in these triangles . 13. ( a ) In a right - angled triangle the hypotenuse is 35 yd . and the per- pendicular is 15 yd .; calculate the ratios specified in Ex . 8 , Art . 8 . ( b ) ...
Página 17
... four methods referred to is the easiest , and which the more exact . Find the air - line distances be- tween places by measuring the distances between them on maps . Several maps may by used so as to have a variety of scales . NOTE ...
... four methods referred to is the easiest , and which the more exact . Find the air - line distances be- tween places by measuring the distances between them on maps . Several maps may by used so as to have a variety of scales . NOTE ...
Página 25
... four places of decimals , in others to five , six , or seven places . There are also tables of the logarithms of the ratios ( or of the logarithms in- creased by 10 ) , which vary in the number of places of decimals to which the ...
... four places of decimals , in others to five , six , or seven places . There are also tables of the logarithms of the ratios ( or of the logarithms in- creased by 10 ) , which vary in the number of places of decimals to which the ...
Página 44
... [ Four - place tables . ] tan A = a 42 = .7500 . .. A 36 ° 52'.2 . b 56 A. .. B 53 ° 7'.8 . ... c = = 70 ft . B90 c = √ a2 + b2 = √1764 + 3136 . A b = 56 Ft . FIG . 16 . Check : C a = c cos B = 70 x cos 53 ° 7.8 70 x .6000 = 42 ft . II ...
... [ Four - place tables . ] tan A = a 42 = .7500 . .. A 36 ° 52'.2 . b 56 A. .. B 53 ° 7'.8 . ... c = = 70 ft . B90 c = √ a2 + b2 = √1764 + 3136 . A b = 56 Ft . FIG . 16 . Check : C a = c cos B = 70 x cos 53 ° 7.8 70 x .6000 = 42 ft . II ...
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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'.