Elements of Trigonometry: Plane and SphericalHarper & brothers, 1898 - 138 páginas Carl J. Martinson collection. |
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Página 73
... -x e sinh = > 2 ex + -x cosh x = 2 ( 15 ) ( 16 ) in which sinhr and coshr denote the hyperbolic sine and hyperbolic cosine of x respectively . These functions are called THE ROOTS OF UNITY 73 133 The Hyperbolic Functions.
... -x e sinh = > 2 ex + -x cosh x = 2 ( 15 ) ( 16 ) in which sinhr and coshr denote the hyperbolic sine and hyperbolic cosine of x respectively . These functions are called THE ROOTS OF UNITY 73 133 The Hyperbolic Functions.
Página 75
... cosh x , ( 23 ) 2 i ( ex — e ̄x ) sin ix = _ i sinh x 2 ( 24 ) If we compute the value of ex by the aid of series ( 4 ) for a succession of values of x , we find that sinh and cosh x are represented by the curves on page 76 . The system ...
... cosh x , ( 23 ) 2 i ( ex — e ̄x ) sin ix = _ i sinh x 2 ( 24 ) If we compute the value of ex by the aid of series ( 4 ) for a succession of values of x , we find that sinh and cosh x are represented by the curves on page 76 . The system ...
Página 76
... cosh y + cosh c sinh y . Example . — sinhx + sinh y = −i ( sin2x + sin y ) , = — ¿ 2 sin § ¿ ( x + y ) cos § i ( x − y ) , = 2sinh } ( t + y ) cosh } ( t − y ) . Жу sinh 0 cosh x EXERCISES ( 4. ) ( 5. ) ( 6. ) 76 PLANE TRIGONOMETRY.
... cosh y + cosh c sinh y . Example . — sinhx + sinh y = −i ( sin2x + sin y ) , = — ¿ 2 sin § ¿ ( x + y ) cos § i ( x − y ) , = 2sinh } ( t + y ) cosh } ( t − y ) . Жу sinh 0 cosh x EXERCISES ( 4. ) ( 5. ) ( 6. ) 76 PLANE TRIGONOMETRY.
Página 77
... cosh πi = 0 . ( 3. ) Prove sinh πio , cosh πi = —I . Prove that sin ( — ix ) = — sin ix . cos ( -ix ) = cos ix . sinh ( −x ) = − sinh . cosh ( x ) = cosh x . Remark . The hyperbolic tangent , cotangent , secant , and cosecant are ...
... cosh πi = 0 . ( 3. ) Prove sinh πio , cosh πi = —I . Prove that sin ( — ix ) = — sin ix . cos ( -ix ) = cos ix . sinh ( −x ) = − sinh . cosh ( x ) = cosh x . Remark . The hyperbolic tangent , cotangent , secant , and cosecant are ...
Página 122
... cosh x = 2 eix eix = cos x + sin x . -e -ix sin x = 2 i eix + e - ix COS X = 2 i ( ex - e - x ) sin ix = = isinh , 2 exte -x cos ix = = cosh x . 2 SPHERICAL TRIANGLES RIGHT AND QUADRANTAL TRIANGLES ( §§ 83 , 87 ) Use Napier's rules ...
... cosh x = 2 eix eix = cos x + sin x . -e -ix sin x = 2 i eix + e - ix COS X = 2 i ( ex - e - x ) sin ix = = isinh , 2 exte -x cos ix = = cosh x . 2 SPHERICAL TRIANGLES RIGHT AND QUADRANTAL TRIANGLES ( §§ 83 , 87 ) Use Napier's rules ...
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Términos y frases comunes
angle less angle of elevation angle opposite celestial equator celestial sphere circle colog comp cos² cos³ cosc cosh cosx cosy cotangent Cotg cotx decimal ecliptic equal find the angles Find the area Find the distance Find the height formulas greater than 90 Hence hyperbolic functions hypotenuse included angle initial line L.Tang latitude light-house log cot LOGARITHMS OF NUMBERS loge longitude mantissa meridian miles Napier's rules negative OBLIQUE TRIANGLES obtain perpendicular plane polar triangle pole positive Prove quadrantal triangle radians radius Required the remaining right angle right ascension right spherical triangle right triangle roots of unity secx sin b sin sin² sin³ sine and cosine sinh siny solution spherical triangle ABC spherical trigonometry subtends an angle TABLE tanc Tang tany terminal line TRIGONOMETRIC FUNCTIONS values yards ΙΟ ΙΟΙ ཤྩ
Pasajes populares
Página 93 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Página 62 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Página 143 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Página 17 - The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.
Página 143 - Root of a Number: Divide the logarithm of the number by the index of the root ; the quotient is the logarithm of the required root of the number.
Página 51 - If 2 men start from the same place and travel in opposite directions, one at the rate of 4 miles an hour, and the other at the rate of 5 miles an hour, how far apart will they be at the end of 1 hour ? At the end of 2 hours ? 5 hours?
Página 143 - Hence, all numbers that differ only in the position of the decimal point have the same significant part. For example, .002103...
Página 62 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 62 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Página 49 - BCA were measured and found to be 322.55 yd., 60° 34', and 56° 10' respectively. Find the distance AB. 10. A balloon is directly over a straight level road, and between two points on the road from which it is observed. The points are 15847 ft. apart, and the angles of elevation are found to be 49° 12' and 53° 29