Plane Trigonometry, for Colleges and Secondary Schools |
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Page vi
... exercises . Throughout the work the author has endeavoured to make each step clear , and thus to prevent the appearance of that puzzled feeling which has such a depressing influence on those entering upon a new study . On the other hand ...
... exercises . Throughout the work the author has endeavoured to make each step clear , and thus to prevent the appearance of that puzzled feeling which has such a depressing influence on those entering upon a new study . On the other hand ...
Page vii
... exercises suitable for practice and review on the separate chapters are placed at the end of the book instead of at the ends of the chapters . These collections will be found useful , both in the short reviews that may be required on ...
... exercises suitable for practice and review on the separate chapters are placed at the end of the book instead of at the ends of the chapters . These collections will be found useful , both in the short reviews that may be required on ...
Page ix
... Exercises in logarithmic computation CHAPTER II . 224 5 6 TRIGONOMETRIC RATIOS OF ACUTE ANGLES . 8. Ratio . Measure 9 9. Incommensurable quantities . Approximations 12 10. Linear measure . Drawing to scale . Direct measurement by means ...
... Exercises in logarithmic computation CHAPTER II . 224 5 6 TRIGONOMETRIC RATIOS OF ACUTE ANGLES . 8. Ratio . Measure 9 9. Incommensurable quantities . Approximations 12 10. Linear measure . Drawing to scale . Direct measurement by means ...
Page xiii
... Exercises on inverse functions 90. Trigonometric equations PAGE 146 146 148 149 151 152 154 CHAPTER XII . MISCELLANEOUS THEOREMS AND EXERCISES . 92. Functions of twice an angle . Functions of half an angle 93. Functions of three times ...
... Exercises on inverse functions 90. Trigonometric equations PAGE 146 146 148 149 151 152 154 CHAPTER XII . MISCELLANEOUS THEOREMS AND EXERCISES . 92. Functions of twice an angle . Functions of half an angle 93. Functions of three times ...
Page 6
... Exercises in logarithmic computation . On looking at the laws of logarithms , ( 3 ) - ( 6 ) , Art . 3 , it is apparent that logarithms cannot assist in the operations of addition and subtraction . Log- arithms are of no service in ...
... Exercises in logarithmic computation . On looking at the laws of logarithms , ( 3 ) - ( 6 ) , Art . 3 , it is apparent that logarithms cannot assist in the operations of addition and subtraction . Log- arithms are of no service in ...
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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'.