Plane Trigonometry, for Colleges and Secondary Schools |
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Page 15
... give an accurate idea of the relations of certain lines and positions . Maps and architects ' plans are familiar examples of such drawings . In a map an inch may represent 1 mile , 10 miles , 100 miles , 500 miles , and so on , accord ...
... give an accurate idea of the relations of certain lines and positions . Maps and architects ' plans are familiar examples of such drawings . In a map an inch may represent 1 mile , 10 miles , 100 miles , 500 miles , and so on , accord ...
Page 16
... gives the ratio of any line in the drawing to the actual line represented . The scale can also be shown graphically by means of a specially marked line . Both the latter methods are illustrated , for instance , on the map of the Kingdom ...
... gives the ratio of any line in the drawing to the actual line represented . The scale can also be shown graphically by means of a specially marked line . Both the latter methods are illustrated , for instance , on the map of the Kingdom ...
Page 21
... Chapter V. the trigonometric ratios are defined for angles in general . The definitions give in this article will be found to follow immediately from those given in Art . 40 . cot A , sec A , cosec A ( or 12. ] 21 THE TRIGONOMETRIC RATIOS .
... Chapter V. the trigonometric ratios are defined for angles in general . The definitions give in this article will be found to follow immediately from those given in Art . 40 . cot A , sec A , cosec A ( or 12. ] 21 THE TRIGONOMETRIC RATIOS .
Page 23
... give the trigonometric ratios of angle AMP . Note what ratios of angles A and P are equal . 2. In Figs . 45 a , 45 b , Art . 46 , give the trigonometric ratios of the various acute angles . 3. Find the trigonometric ratios of the acute ...
... give the trigonometric ratios of angle AMP . Note what ratios of angles A and P are equal . 2. In Figs . 45 a , 45 b , Art . 46 , give the trigonometric ratios of the various acute angles . 3. Find the trigonometric ratios of the acute ...
Page 40
... gives a fair approximation to the result . This result will sometimes show that there is an error in the result obtained by computation . A little error in arithmetic may yield a quantity which is ten times too great or too small ; but ...
... gives a fair approximation to the result . This result will sometimes show that there is an error in the result obtained by computation . A little error in arithmetic may yield a quantity which is ten times too great or too small ; but ...
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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'.