Plane Trigonometry, for Colleges and Secondary Schools |
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Page v
... contain a great variety of matters which it is impossible to consider in the time usually assigned to this study in school and college . On the other hand , the expla- nations given in many other works are so meagre that the stu- dent ...
... contain a great variety of matters which it is impossible to consider in the time usually assigned to this study in school and college . On the other hand , the expla- nations given in many other works are so meagre that the stu- dent ...
Page vi
... contain little more about trigonometric ratios and angular analysis than is sufficient to enable the beginner to understand clearly the arithmetical part of the science , and its simple practical applica- tions . This arrangement seems ...
... contain little more about trigonometric ratios and angular analysis than is sufficient to enable the beginner to understand clearly the arithmetical part of the science , and its simple practical applica- tions . This arrangement seems ...
Page 10
... contain 10 yards ? What fraction of 10 yards is 3 weeks ? When it is said that a line is ten inches long , this statement means that a line one inch long has been chosen for the unit of length , and that the first line contains ten of ...
... contain 10 yards ? What fraction of 10 yards is 3 weeks ? When it is said that a line is ten inches long , this statement means that a line one inch long has been chosen for the unit of length , and that the first line contains ten of ...
Page 17
... contain different numbers of divisions to an inch , one 10 divisions , one 20 , one 30 , and so on ; and generally , one inch on each face is subdivided so that a small fraction of an inch may be set off or read . Some paper scales are ...
... contain different numbers of divisions to an inch , one 10 divisions , one 20 , one 30 , and so on ; and generally , one inch on each face is subdivided so that a small fraction of an inch may be set off or read . Some paper scales are ...
Page 18
... containing 37 degrees and 42 minutes and 35 seconds , say , is written thus : 37 ° 42 ' 35 ' , read 37 degrees , 42 ... contain between 0 ° and 90 ° , are considered . Chapter V. considers angles of all magnitudes . NOTE 1. An angle 1o ...
... containing 37 degrees and 42 minutes and 35 seconds , say , is written thus : 37 ° 42 ' 35 ' , read 37 degrees , 42 ... contain between 0 ° and 90 ° , are considered . Chapter V. considers angles of all magnitudes . NOTE 1. An angle 1o ...
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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'.