A system of popular trigonometry1835 |
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Página 44
... cotan A = R2 . DEM . The angles HAC , ACB , CBK , being all right an- gles , AH is parallel to CB , and AC to вK . Consequently , by ART . 12 , GEOM . the angle ACH = the angle CKB , and the angle AHC = the angle HCB . Therefore , by ...
... cotan A = R2 . DEM . The angles HAC , ACB , CBK , being all right an- gles , AH is parallel to CB , and AC to вK . Consequently , by ART . 12 , GEOM . the angle ACH = the angle CKB , and the angle AHC = the angle HCB . Therefore , by ...
Página 45
... of A , COS A cotan A R sin A In other words , the ratio of the cosine to the sine of an angle is the same as that of the cotangent to the radius . ART . 5. The rectangle under the secant and cosine FUNDAMENTAL THEOREMS . 45.
... of A , COS A cotan A R sin A In other words , the ratio of the cosine to the sine of an angle is the same as that of the cotangent to the radius . ART . 5. The rectangle under the secant and cosine FUNDAMENTAL THEOREMS . 45.
Página 47
... cotan ACD ' = R2 . sin2 ACD ' + cos2 ACD ' = R2 . sin ACD ' tan ACD ' · COS ACD ' COS ACD ' sin ACD ' R • ( ART . 4. ) ( Obs . cotan ACD ' R sec ACD ' x cos ACD ' = R2 . cosec ACD ' X sin ACD ' = R2 . DEF . VI . The supplement of an ...
... cotan ACD ' = R2 . sin2 ACD ' + cos2 ACD ' = R2 . sin ACD ' tan ACD ' · COS ACD ' COS ACD ' sin ACD ' R • ( ART . 4. ) ( Obs . cotan ACD ' R sec ACD ' x cos ACD ' = R2 . cosec ACD ' X sin ACD ' = R2 . DEF . VI . The supplement of an ...
Página 52
... cotan A = R2 . 4 . sin2 A + cos2 A = R2 . sin A tan A 5 . COS A R COS A cotan A 6 . sin A R 7 . sec A X cos A = R2 . 8 . cosec A X sin A = R2 . 9 . RX sin 2A = 2 sin A × cos A. 10 . RX cos 2A = ― R2 2 sin2 A. 11 . RX COS A = R2 - 2 sin2 ...
... cotan A = R2 . 4 . sin2 A + cos2 A = R2 . sin A tan A 5 . COS A R COS A cotan A 6 . sin A R 7 . sec A X cos A = R2 . 8 . cosec A X sin A = R2 . 9 . RX sin 2A = 2 sin A × cos A. 10 . RX cos 2A = ― R2 2 sin2 A. 11 . RX COS A = R2 - 2 sin2 ...
Página 53
... cotan 45 ° = R2 , by ART . 10 ; cotan 45 ° = R. ART . 11. The sine is equal to the cosine.
... cotan 45 ° = R2 , by ART . 10 ; cotan 45 ° = R. ART . 11. The sine is equal to the cosine.
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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...