Plane Trigonometry, for Colleges and Secondary Schools |
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Page 4
... Hence , if the logarithms ( i.e. the exponents of powers ) of num- bers be used instead of the numbers themselves , then the opera- tions of multiplication and division are replaced by those of addition and subtraction , and the ...
... Hence , if the logarithms ( i.e. the exponents of powers ) of num- bers be used instead of the numbers themselves , then the opera- tions of multiplication and division are replaced by those of addition and subtraction , and the ...
Page 5
... hence , log 25.38 = log 2538-2 , log 2538000 = log 2538 +3 . Accordingly , it is necessary to put only the mantissas of se- quences of integers in the tables . 5. Negative characteristics . In common logarithms the mantissa is always ...
... hence , log 25.38 = log 2538-2 , log 2538000 = log 2538 +3 . Accordingly , it is necessary to put only the mantissas of se- quences of integers in the tables . 5. Negative characteristics . In common logarithms the mantissa is always ...
Page 18
... Hence comes the following table of angular measure : 1 minute , 60 seconds 60 minutes 90 degrees - 1 degree , = = 1 right angle . The magnitude of an angle containing 37 degrees and 42 minutes and 35 seconds , say , is written thus : 37 ...
... Hence comes the following table of angular measure : 1 minute , 60 seconds 60 minutes 90 degrees - 1 degree , = = 1 right angle . The magnitude of an angle containing 37 degrees and 42 minutes and 35 seconds , say , is written thus : 37 ...
Page 21
... hence six ratios can be formed with them , namely : MP AM MP AM AP AP · 9 AP AP AM MP AM MP It is 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 ...
... hence six ratios can be formed with them , namely : MP AM MP AM AP AP · 9 AP AP AM MP AM MP It is 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 ...
Page 24
... Hence the sides about the equal angles are propor- tional , and MP ST KG = = AP AS BG Therefore all angles equal to A have the same sine . In like manner , these angles can be shown to have the same tangent , secant , etc. * L1 R L A M1 ...
... Hence the sides about the equal angles are propor- tional , and MP ST KG = = AP AS BG Therefore all angles equal to A have the same sine . In like manner , these angles can be shown to have the same tangent , secant , etc. * L1 R L A M1 ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 122 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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'.