Plane Trigonometry, for Colleges and Secondary Schools |
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Page ix
... Definition of a logarithm . 3. Properties of logarithms . 4. Common system of logarithms 5. Negative characteristics 6. Exercises in logarithmic computation CHAPTER II . 224 5 6 TRIGONOMETRIC RATIOS OF ACUTE ANGLES . 8. Ratio . Measure ...
... Definition of a logarithm . 3. Properties of logarithms . 4. Common system of logarithms 5. Negative characteristics 6. Exercises in logarithmic computation CHAPTER II . 224 5 6 TRIGONOMETRIC RATIOS OF ACUTE ANGLES . 8. Ratio . Measure ...
Page x
... definition of an angle . Angles unlimited in magni- tude . Positive and negative angles 38. Supplement and complement of an angle 29. The convention of signs on a plane . 40. General definition of the trigonometric ratios . 5822 67 69 ...
... definition of an angle . Angles unlimited in magni- tude . Positive and negative angles 38. Supplement and complement of an angle 29. The convention of signs on a plane . 40. General definition of the trigonometric ratios . 5822 67 69 ...
Page xii
... definitions of the trigonometric functions 135 80. Geometrical representation of the trigonometric functions 81. Graphical representation of functions 137 138 82. Graphs of the trigonometric functions 139 83. Relations between the ...
... definitions of the trigonometric functions 135 80. Geometrical representation of the trigonometric functions 81. Graphical representation of functions 137 138 82. Graphs of the trigonometric functions 139 83. Relations between the ...
Page xiii
... definitions of trigonometric ratios . NOTE C. On the ratio of the length of a circle to its diameter NOTE D. On analytical trigonometry and De Moivre's Theorem QUESTIONS AND EXERCISES FOR PRACTICE AND REVIEW ANSWERS TO THE EXAMPLES ...
... definitions of trigonometric ratios . NOTE C. On the ratio of the length of a circle to its diameter NOTE D. On analytical trigonometry and De Moivre's Theorem QUESTIONS AND EXERCISES FOR PRACTICE AND REVIEW ANSWERS TO THE EXAMPLES ...
Page 1
... , but erroneously , as Napierian logarithms . See historical sketch in article Logarithms ( Ency . Brit . 9th edition ) , by J. W. L. Glaisher . 2. Definition of a logarithm . If ax = N 1 CHAPTER REVIEW OF LOGARITHMS.
... , but erroneously , as Napierian logarithms . See historical sketch in article Logarithms ( Ency . Brit . 9th edition ) , by J. W. L. Glaisher . 2. Definition of a logarithm . If ax = N 1 CHAPTER REVIEW OF LOGARITHMS.
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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'.