The Elements of Plane TrigonometryJ. Weale, 1854 - 119 páginas |
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Página 8
... less than two , then bp is called the sine ; Cp the cosine ; AR the tangent ; CR the secant ; Ap the versed sine . If the arc Abd be greater than two quadrants but less than three , then de r e g P T T ' B D R C is called the sine ; Ce ...
... less than two , then bp is called the sine ; Cp the cosine ; AR the tangent ; CR the secant ; Ap the versed sine . If the arc Abd be greater than two quadrants but less than three , then de r e g P T T ' B D R C is called the sine ; Ce ...
Página 29
... less , we have Putting - A = ↓ ( A + B ) + ¦ ( A − B ) , B = { ( A + B ) - ( A + B ) for A , and ( A + B ) and cos ( A + B ) ; = 1 ( A – B ) . ( A – B ) for B , in sin - sin A = sin { ( A + B ) + 1⁄2 ( A − B ) } - · sin 1 ( A + B ) ...
... less , we have Putting - A = ↓ ( A + B ) + ¦ ( A − B ) , B = { ( A + B ) - ( A + B ) for A , and ( A + B ) and cos ( A + B ) ; = 1 ( A – B ) . ( A – B ) for B , in sin - sin A = sin { ( A + B ) + 1⁄2 ( A − B ) } - · sin 1 ( A + B ) ...
Página 33
... less than 45o , sin A is less than cos A. By adding , 2 cos A = √ ( 1 + sin 2A ) + √ ( 1 − sin 2A ) , A 1 cos △ = 11⁄2 √ / ( 1 + sin 24 ) + 1⁄2 √ ( 1 − sin 24 ) . Subtracting , 2 sin A = ( 1 + sin 2A ) - ( 1 - sin 2A ) , - 1 sin ...
... less than 45o , sin A is less than cos A. By adding , 2 cos A = √ ( 1 + sin 2A ) + √ ( 1 − sin 2A ) , A 1 cos △ = 11⁄2 √ / ( 1 + sin 24 ) + 1⁄2 √ ( 1 − sin 24 ) . Subtracting , 2 sin A = ( 1 + sin 2A ) - ( 1 - sin 2A ) , - 1 sin ...
Página 38
... less than 45o . Now , in the above formula let A = 9o , then , 2 A = 18o , 1 - sin 9o = { √ / ( 1 + sin 18 ° ) — √ / ( 1 − sin 18o ) } = 2 1+ - - { // ( 1 + 2/5 - 1 ) - √ / ( 1 - 1/5 - 1 ) } - = ¦ { √ ( 3 + √5 ) − √ ( 5 − √5 ) ...
... less than 45o . Now , in the above formula let A = 9o , then , 2 A = 18o , 1 - sin 9o = { √ / ( 1 + sin 18 ° ) — √ / ( 1 − sin 18o ) } = 2 1+ - - { // ( 1 + 2/5 - 1 ) - √ / ( 1 - 1/5 - 1 ) } - = ¦ { √ ( 3 + √5 ) − √ ( 5 − √5 ) ...
Página 58
... less than unity , ( a + b ) 3 for Jab is less than ( a + b ) * , or ( a + b ) is greater than 4 ab , and since the cosine cannot exceed unity , it is evident that the above is a proper fraction , and we may put sin20 = 4 ab cos2 C ( a + ...
... less than unity , ( a + b ) 3 for Jab is less than ( a + b ) * , or ( a + b ) is greater than 4 ab , and since the cosine cannot exceed unity , it is evident that the above is a proper fraction , and we may put sin20 = 4 ab cos2 C ( a + ...
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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.