The Elements of Plane TrigonometryJ. Weale, 1854 - 119 páginas |
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... radius of the inscribed circle Area of the triangle in terms of the radius of the circumscribed Practical remarks on the solution of triangles ༄ ལྷ 58 59 69 60 75 Polygons CHAPTER IV . 80 CHAPTER V. Demoivre's theorem . 104 TRIGONOMETRY ...
... radius of the inscribed circle Area of the triangle in terms of the radius of the circumscribed Practical remarks on the solution of triangles ༄ ལྷ 58 59 69 60 75 Polygons CHAPTER IV . 80 CHAPTER V. Demoivre's theorem . 104 TRIGONOMETRY ...
Página 2
... radius of the circle Hence the length of the arc of a quadrant is πr of a semi- 2 3πη circle , or 180 ° , is πr ; and of 270 ° , or three quadrants , is 2 πr 2 Now if any arc a subtend an angle of Ao , then since subtends 90 ° , and ...
... radius of the circle Hence the length of the arc of a quadrant is πr of a semi- 2 3πη circle , or 180 ° , is πr ; and of 270 ° , or three quadrants , is 2 πr 2 Now if any arc a subtend an angle of Ao , then since subtends 90 ° , and ...
Página 3
... radius ' ( 2 ) . α which is called the circular measure of the angle . == ↑ From equation ( 2 ) we see that the measuring unit , Uo , must be multiplied by the fraction to find the angle ; a r thus if the circular measure of an angle ...
... radius ' ( 2 ) . α which is called the circular measure of the angle . == ↑ From equation ( 2 ) we see that the measuring unit , Uo , must be multiplied by the fraction to find the angle ; a r thus if the circular measure of an angle ...
Página 5
... radius is 25 feet . A ° - 180 ° a 180 ° 30 180 ° 6 X- = π r = 57 ° • 29578 × X = π 25 6 = 68 ° .75493 . -X ( 6 ) Find the number of degrees in an angle of which the circular measure is 7854 , the value of π being 3 · 1416 . 180 ° a 180 ...
... radius is 25 feet . A ° - 180 ° a 180 ° 30 180 ° 6 X- = π r = 57 ° • 29578 × X = π 25 6 = 68 ° .75493 . -X ( 6 ) Find the number of degrees in an angle of which the circular measure is 7854 , the value of π being 3 · 1416 . 180 ° a 180 ...
Página 8
... radius CB ; CP is called the cosine ; AT the tangent ; CT the se- cant ; AP the versed sine ; OT " the co- tangent ; CT ' the cosecant . If we take the arc Ab greater than one quadrant and less than two , then bp is called the sine ; Cp ...
... radius CB ; CP is called the cosine ; AT the tangent ; CT the se- cant ; AP the versed sine ; OT " the co- tangent ; CT ' the cosecant . If we take the arc Ab greater than one quadrant and less than two , then bp is called the sine ; Cp ...
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Términos y frases comunes
A+ cot a+b+c AB² AC² angle ACB angle of elevation AO² AP AP Asin BOP₁ centre circumference circumscribed cos A cos cos² cos³ cosec cosine cot A cot cot A+ cot² OPA cot³ diameter distance Divide equation feet formula given height hence hexagon inscribed circle logarithms negative nth root number of sides Oa cot OA² OB² perimeter perpendicular plane triangle quadrant r² cot radii radius ratio regular polygon right angle right-angled triangle sec² sector shew sin A cos sin A sin sin-¹ sin² sin² 18 sin³ sine sine and cosine square subtend subtracted tan-¹ tan² tan³ tangent triangle ABC unity ηφ
Pasajes populares
Página 97 - From a window near the bottom of a house, which seemed to be on a level with the bottom of a steeple, I took the angle of elevation of the top of the steeple, equal to 40° ; then from another window, 18 feet directly above the former, the like angle was 37° 30'.
Página 97 - Wanting to know the height of an inaccessible tower; at the least distance from it, on the same horizontal plane, I took its angle of elevation equal to 58°; then going 300 feet directly from it, found the angle there to be only 32°: required its height, and my distance from it at the first station?
Página 86 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Página 51 - It depends on the principle, that the difference of the squares of two quantities is equal to the product of the sum and difference of the quantities.
Página 63 - If from one of the angles of a rectangle a perpendicular be drawn to its diagonal, and from, the point of their intersection lines be drawn perpendicular to the sides which contain the opposite angle...
Página 87 - The square on the side of a regular pentagon inscribed in a circle is equal to the sum of the squares on the sides of the regular hexagon and decagon inscribed in the same circle.
Página 93 - To THEIR DIFFERENCE ; - So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES; To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 98 - Wanting to know my distance from an inaccessible object 0, on the other side of a river; and having no instrument for taking angles, but only a chain or cord for measuring distances; from each of two stations, A and B, which were taken at 500 yards asunder, I measured in a direct line from the object 0 100 yards, viz. AC and BD each equal to 100 yards ; also the diagonal AD measured 550 yards, and the diagonal BC 560. What then was the distance of the object 0 from each, station A and B ? . C AO...
Página 97 - Being on a horizontal plane, and wanting to know the height of a tower placed on the top of an inaccessible hill : I took the angle of elevation of the top of the hill 40°, and of the top of the tower 51°; then measuring in a line directly from it to the distance of 200 feet farther, I found the angle at the top of the tower to be 33° 45'.
Página 101 - The hypotenuse AB of a right-angled triangle ABC is trisected in the points D, E; prove that if CD, CE be joined, the sum of the squares on the sides of the triangle CDE is equal to two-thirds of the square on AB.