Elementary Text-book of TrigonometryBlackie & Son, 1884 - 176 páginas |
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Página 9
... proved if we make the assumption of the preceding Article . For AD and CE being diameters at right angles , the arc AC is circumference or Ꭰ C B E A × 2 , and the angle AOC is a right angle . But by Euclid VI . 33 , angle AOB : angle ...
... proved if we make the assumption of the preceding Article . For AD and CE being diameters at right angles , the arc AC is circumference or Ꭰ C B E A × 2 , and the angle AOC is a right angle . But by Euclid VI . 33 , angle AOB : angle ...
Página 23
... prove from the figure , for tangent and cotangent , and also for secant and cosecant . Thus the co- sine , the cotangent , and the cosecant of an angle are equal respectively to the sine , the tangent , and the secant of the complement ...
... prove from the figure , for tangent and cotangent , and also for secant and cosecant . Thus the co- sine , the cotangent , and the cosecant of an angle are equal respectively to the sine , the tangent , and the secant of the complement ...
Página 33
... proved under the restriction that the angle is less than a right angle . This restriction will be removed in Chapter IV . , where it will be proved that the 8 relations , and therefore all others which may be deduced from them , are ...
... proved under the restriction that the angle is less than a right angle . This restriction will be removed in Chapter IV . , where it will be proved that the 8 relations , and therefore all others which may be deduced from them , are ...
Página 34
... Prove that = ( 1 − sinA ) ( 1 + sinA ) . sinA cosA tan ( 90 ° – A ) + sinA cosA cot ( 90 ° — A ) = 1 . Since tan ( 90 ° -A ) = cotA , and cot ( 90 ° – A ) = tanA , ( Art . 16 ) , sinA cosA tan ( 90 ° – A ) = sinA cosA cotA therefore ...
... Prove that = ( 1 − sinA ) ( 1 + sinA ) . sinA cosA tan ( 90 ° – A ) + sinA cosA cot ( 90 ° — A ) = 1 . Since tan ( 90 ° -A ) = cotA , and cot ( 90 ° – A ) = tanA , ( Art . 16 ) , sinA cosA tan ( 90 ° – A ) = sinA cosA cotA therefore ...
Página 35
... Prove the following formulæ : 1. tan2A = ( secA − 1 ) ( secA + 1 ) . - 2. cot2A = ( cosecA - 1 ) ( cosecA + 1 ) . 3. sinA cos A tanA cotA secA cosecA = 1 . 4. sin A sec ( 90 ° – A ) = 1 . 5. cosA cosec ( 90 ° - A ) = 1 . 6. tanA tan ...
... Prove the following formulæ : 1. tan2A = ( secA − 1 ) ( secA + 1 ) . - 2. cot2A = ( cosecA - 1 ) ( cosecA + 1 ) . 3. sinA cos A tanA cotA secA cosecA = 1 . 4. sin A sec ( 90 ° – A ) = 1 . 5. cosA cosec ( 90 ° - A ) = 1 . 6. tanA tan ...
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Términos y frases comunes
angle AOB angle BAC angle increases angle less Article base centre circumference cloth boards common logarithm complement cos(A+B cos2A cos4A cosB cosC cose cosecA cosine cotA cotangent decimal places degree measure diameter distance equal equation Euclid EXAMPLES feet Find the angle Find the height find the number find the values flagstaff following angles formula given Hence hypotenuse inches log2 loga logarithms of numbers magnitude mantissa miles negative numbers number expressing number of degrees numerical value perpendicular positive Prove quadrant radian measure radii ratios of angles regular polygon respectively right angle right-angled triangle sec²A secA secant side BC Similarly sin(A sin(A+B sin2A sin2B sin3A sinB sine sine and cosine square root table of logarithms tan(A+B tan²A tanA tanB tangent tanß tower triangle ABC trigono trigonometrical ratios unit of angle yards
Pasajes populares
Página 90 - The logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers. For, let m and n be two numbers, and x and y their logarithms. Then, by the definition of a logarithm, m — ax, and n = a".
Página 90 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Página 118 - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Página 149 - Find the length of the side of a square whose area is equal to that of a rectangle the sides of which are 94 '28 and 6720 yards.
Página 89 - The logarithm of a number is the index of the power to which the base of the system must be raised to equal a given number.
Página 158 - The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 : 5.