A system of popular trigonometry1835 |
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Página 65
... cotan A¦R x : y :: : 1 , y d : 1 ; y and , CD DG cosec AR :: d : y hence we may write numeral tangent , secant , cotangent , and cosecant of an angle as follows : tan A = y SEC A = cotan A = ४ । y । ৯৪ d Cosec A y Both the linear ...
... cotan A¦R x : y :: : 1 , y d : 1 ; y and , CD DG cosec AR :: d : y hence we may write numeral tangent , secant , cotangent , and cosecant of an angle as follows : tan A = y SEC A = cotan A = ४ । y । ৯৪ d Cosec A y Both the linear ...
Página 66
... cotan 2A . y Ꮳ 3o . tan A X cotan A = X = 1 . y y2 x2 4o . sin2 A + cos2 A = + = d2 de y2 + x2 d2 || d2 1 . d2 sin A 5o . y XC y = - = tan A. COS A x COS A 6o . = sin A 88 y d ÷ = d XC y = cotan A. d X 70. sec A X cos A = X d = 1 . d ...
... cotan 2A . y Ꮳ 3o . tan A X cotan A = X = 1 . y y2 x2 4o . sin2 A + cos2 A = + = d2 de y2 + x2 d2 || d2 1 . d2 sin A 5o . y XC y = - = tan A. COS A x COS A 6o . = sin A 88 y d ÷ = d XC y = cotan A. d X 70. sec A X cos A = X d = 1 . d ...
Página 69
... cotan A = 1 . 4. sin2 A + cos2 A = 1 . sin A 5 . = tan A. COS A COS A 6 . = cotan A. sin A 7. sec A. cos A = 1 . 8. cosec A. sin A = 1 . 9. sin 2A = 2 sin A COS A. 10. cos 2A = 1 2 sin2 A. - A 11. cos A = 1 - 2 sin2 12. 1+ cos A = 2 ...
... cotan A = 1 . 4. sin2 A + cos2 A = 1 . sin A 5 . = tan A. COS A COS A 6 . = cotan A. sin A 7. sec A. cos A = 1 . 8. cosec A. sin A = 1 . 9. sin 2A = 2 sin A COS A. 10. cos 2A = 1 2 sin2 A. - A 11. cos A = 1 - 2 sin2 12. 1+ cos A = 2 ...
Página 107
... cotan c , sin c or , by ART . 11 , this equation becomes tan BX COS C = cotan c cos b .. tan в X cos cx cos b = cotan c ; tan B X cos a cotan C , which is a third new formula . COS C Again : inasmuch as cotan c = sin c we get from this ...
... cotan c , sin c or , by ART . 11 , this equation becomes tan BX COS C = cotan c cos b .. tan в X cos cx cos b = cotan c ; tan B X cos a cotan C , which is a third new formula . COS C Again : inasmuch as cotan c = sin c we get from this ...
Página 108
... cotan c = sin b × cotan c , or as cotan = 1 sin b tan c tan c 1 tan ' .. tan c = tan cx sin b ; a result perfectly symmetrical with the fourth new for- mula , and which might have been deduced at once from that by changing в , c , b ...
... cotan c = sin b × cotan c , or as cotan = 1 sin b tan c tan c 1 tan ' .. tan c = tan cx sin b ; a result perfectly symmetrical with the fourth new for- mula , and which might have been deduced at once from that by changing в , c , b ...
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Palavras e frases frequentes
ABCD AC AC algebraical quantities angle ACD angle bac angle is equal angular CD² centre compute Consequently corresponding cos² cosec cosine of ACD cotan determine the magnitude dicular DIONYSIUS LARDNER divided EFGH equal to half equal to one-third equation figure formula GEOM geometric series geometrical given angle goniometrical circle goniometrical lines half a right Hence inasmuch inscribed square length Let ACD likewise linear unit logarithms means opposite parallelopiped perpen perpendicular plane ABO prec radius ratio rectangle respectively right angle right-angled triangle sec² secant sides and angles sin² sine of ACD sphere submultiple subtractive supplementary angles suppose tan² tangent third side three sides Treatise triangle ABC TRIGONOMETRY
Passagens conhecidas
Página 110 - PRINCIPLES OF GEOMETRY, familiarly Illustrated, and applied to a variety of useful purposes. Designed for the Instruction of Young Persons.
Página 111 - I vol. 8vo. THE STEAM ENGINE. Explained and illustrated in a familiar style, with its application to the Arts and Manufactures, more especially in transport by Land and Water ; with some account of the Rail Roads now in progress in various parts of the World. By the Rev. DIONYSIUS LARDNER, LL.
Página vi - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Página iii - A straight line is said to be perpendicular to a plane when it is perpendicular to every straight line which passes through its foot in that plane, and the plane is said to be perpendicular to the line.
Página 5 - Now, we know that the three angles of any triangle, taken together, are equal to two right angles...
Página 110 - Dr. Ritchie's little elementary work is excellently well adapted to its object. It is brief, plain, and full of all that is necessary : curious and useful in its application ; and beyond any other of the kind now existent in its familiar and distinct explanation of some of the instruments required in the practical application of the principles laid down and demonstrated.
Página 53 - We have, then, that the sine of an angle is equal to the cosine of its complement, and conversely.
Página iii - THEOREM. Every section of a sphere, made by a plane, is a circle.
Página 37 - The sum of the squares of the sine and cosine of an angle is...