Plane Trigonometry, for Colleges and Secondary Schools |
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Page xi
... included angle 102 105 58. Case IV . Given three sides 105 59. The aid of logarithms in the solution of triangles 60. The use of logarithms in Cases I. , II . 61. Relation between the sum and the difference of any two sides of a ...
... included angle 102 105 58. Case IV . Given three sides 105 59. The aid of logarithms in the solution of triangles 60. The use of logarithms in Cases I. , II . 61. Relation between the sum and the difference of any two sides of a ...
Page 9
... included in the subject of trigonometry . The more ele- mentary part of trigonometry is concerned with the calculation of straight and circular lines , angles , and areas belonging to figures on planes and spheres . It consists of two ...
... included in the subject of trigonometry . The more ele- mentary part of trigonometry is concerned with the calculation of straight and circular lines , angles , and areas belonging to figures on planes and spheres . It consists of two ...
Page 38
... included angle is 28 ° 30 ' ; the third side and the other angles are required . The graphical solution is as follows : Construct a triangle QPR having two sides , PQ , PR , representing 10 ft . , 5 ft . , respectively , on some con- 38 ...
... included angle is 28 ° 30 ' ; the third side and the other angles are required . The graphical solution is as follows : Construct a triangle QPR having two sides , PQ , PR , representing 10 ft . , 5 ft . , respectively , on some con- 38 ...
Page 39
... included angle , QPR , equal to 28 ° 30 ' , as Measure the angles PRQ , PQR with the protractor ; measure the side RQ and , by reference to the scale , find the length represented by RQ . [ The results thus obtained may be compared with ...
... included angle , QPR , equal to 28 ° 30 ' , as Measure the angles PRQ , PQR with the protractor ; measure the side RQ and , by reference to the scale , find the length represented by RQ . [ The results thus obtained may be compared with ...
Page 54
... 4. Find area of parallelogram two of whose adjacent sides are 243 , 315 yd . , and their included angle 35 ° 40 ' . 5. Find area of parallelogram two of whose adjacent sides 54 [ CH . IV . PLANE TRIGONOMETRY . Mensuration.
... 4. Find area of parallelogram two of whose adjacent sides are 243 , 315 yd . , and their included angle 35 ° 40 ' . 5. Find area of parallelogram two of whose adjacent sides 54 [ CH . IV . PLANE TRIGONOMETRY . Mensuration.
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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'.