Plane Trigonometry, for Colleges and Secondary Schools |
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Page vii
... notes ; and an historical sketch is given in the Appendix . It is believed that some knowledge of the historical development of trigonome- try , and of the men of various times and races who have helped to advance the subject , will ...
... notes ; and an historical sketch is given in the Appendix . It is believed that some knowledge of the historical development of trigonome- try , and of the men of various times and races who have helped to advance the subject , will ...
Page xii
... note 129 77. Changes in the trigonometric functions as the angle increases from 0 ° to 360 ° 131 78. Periodicity of the trigonometric functions 134 79. The old or line definitions of the trigonometric functions 135 80. Geometrical ...
... note 129 77. Changes in the trigonometric functions as the angle increases from 0 ° to 360 ° 131 78. Periodicity of the trigonometric functions 134 79. The old or line definitions of the trigonometric functions 135 80. Geometrical ...
Page xiii
... NOTE A. Historical sketch NOTE B. Projection 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 ...
... NOTE A. Historical sketch NOTE B. Projection 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 ...
Page 7
... by 2 , = log 456 2.65896 , log 350 = 2.54407 log 372 - 2.57054 , log 249 - = 2.39620 5.22950 4.94027 4.94027 2.28923 ... log R = .14462 ( See Art . 9 , Note 1. ) ... R = 1.395 . 5. Find the value of x in 34 * = 6.1 7 EXERCISES .
... by 2 , = log 456 2.65896 , log 350 = 2.54407 log 372 - 2.57054 , log 249 - = 2.39620 5.22950 4.94027 4.94027 2.28923 ... log R = .14462 ( See Art . 9 , Note 1. ) ... R = 1.395 . 5. Find the value of x in 34 * = 6.1 7 EXERCISES .
Page 12
... and sufficient . For example , in calculating a length in inches in ordinary engineer- * See Appendix , Note C. ing work there is no need to go beyond the 12 [ CH . II . PLANE TRIGONOMETRY . Incommensurable quantities Approximations.
... and sufficient . For example , in calculating a length in inches in ordinary engineer- * See Appendix , Note C. ing work there is no need to go beyond the 12 [ CH . II . PLANE TRIGONOMETRY . Incommensurable quantities Approximations.
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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'.