Plane Trigonometry, for Colleges and Secondary Schools |
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Page 18
... subtended by 1 in . at a distance 4 ft . 9.3 in . , and by 1 ft . at a distance 57.3 ft . An angle 1 ' is subtended by 1 in . at a distance 286.5 ft . , and by 1 ft . at a distance 3437.6 ft . , about two - thirds of a mile . An angle 1 ...
... subtended by 1 in . at a distance 4 ft . 9.3 in . , and by 1 ft . at a distance 57.3 ft . An angle 1 ' is subtended by 1 in . at a distance 286.5 ft . , and by 1 ft . at a distance 3437.6 ft . , about two - thirds of a mile . An angle 1 ...
Page 22
... circular arcs sub- tended by the angle . This is explained in Art . 79 , which the student can easily read at this time . See Art . 80 , Notes 2 , 3 . sin A = opposite side , hypotenuse , cos A 22 [ Сн . ІІ . PLANE TRIGONOMETRY .
... circular arcs sub- tended by the angle . This is explained in Art . 79 , which the student can easily read at this time . See Art . 80 , Notes 2 , 3 . sin A = opposite side , hypotenuse , cos A 22 [ Сн . ІІ . PLANE TRIGONOMETRY .
Page 52
... subtends an angle 34 ° 45 ' , and its length subtends an angle 72 ° 30 ' ; the height of the house is 48 ft . Find its length . 30. Problems requiring a knowledge of the points of the 52 [ CH . IV . PLANE TRIGONOMETRY .
... subtends an angle 34 ° 45 ' , and its length subtends an angle 72 ° 30 ' ; the height of the house is 48 ft . Find its length . 30. Problems requiring a knowledge of the points of the 52 [ CH . IV . PLANE TRIGONOMETRY .
Page 114
... subtended by the distance of the objects being 55 ° 40 ' . 4. The distance of a station from two objects situated at opposite sides of a hill are 1128 and 936 yd . , and the angle subtended at the station by their distance , is 64 ° 28 ...
... subtended by the distance of the objects being 55 ° 40 ' . 4. The distance of a station from two objects situated at opposite sides of a hill are 1128 and 936 yd . , and the angle subtended at the station by their distance , is 64 ° 28 ...
Page 115
... subtends an angle a at a point on the same level as the foot of the tower and , at a second point , h feet above the first , the depression of the foot of the tower is B. Show that the height of the tower is h tan a cot ß . 13. The ...
... subtends an angle a at a point on the same level as the foot of the tower and , at a second point , h feet above the first , the depression of the foot of the tower is B. Show that the height of the tower is h tan a cot ß . 13. The ...
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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'.