Elements of Trigonometry: Plane and SphericalHarper & brothers, 1898 - 138 páginas Carl J. Martinson collection. |
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... Difference of Two Angles . Functions of Twice an Angle Functions of Half an Angle . Formulas for the Sums and Differences of Functions The Inverse Trigonometric Functions • +36 338 32 36 36 37 · 39 CHAPTER IV THE OBLIQUE TRIANGLE ...
... Difference of Two Angles . Functions of Twice an Angle Functions of Half an Angle . Formulas for the Sums and Differences of Functions The Inverse Trigonometric Functions • +36 338 32 36 36 37 · 39 CHAPTER IV THE OBLIQUE TRIANGLE ...
Página 35
... ° . ( 9. ) Given sin 45 ° = √√2 , cos 45 ° = √2 ; find sin 90 ° and cos 90o . ( 10. ) Prove that_sin ( 60 ° + x ) — sin ( 60 ° — x ) = sin x . TANGENT OF THE SUM AND DIFFERENCE OF TWO ANGLES 35. TRIGONOMETRIC ANALYSIS 35.
... ° . ( 9. ) Given sin 45 ° = √√2 , cos 45 ° = √2 ; find sin 90 ° and cos 90o . ( 10. ) Prove that_sin ( 60 ° + x ) — sin ( 60 ° — x ) = sin x . TANGENT OF THE SUM AND DIFFERENCE OF TWO ANGLES 35. TRIGONOMETRIC ANALYSIS 35.
Página 36
... DIFFERENCE OF TWO ANGLES 35. Tan ( x + y ) = = sin ( r + y ) _ sint cosy + cost sin y cos ( x + y ) cosx cos y − sin x sing Dividing each term of both numerator and denominator of the right - hand side of this equation by cosa cosy ...
... DIFFERENCE OF TWO ANGLES 35. Tan ( x + y ) = = sin ( r + y ) _ sint cosy + cost sin y cos ( x + y ) cosx cos y − sin x sing Dividing each term of both numerator and denominator of the right - hand side of this equation by cosa cosy ...
Página 37
... DIFFERENCES OF FUNCTIONS 38. From formulas ( 11 ) – ( 14 ) , we obtain Let then - sin ( x + y ) + sin ( x − y ) = 2 sin x cosy ; - sin ( x + y ) —sin ( x − y ) = 2 cosx siny ; cos ( x + y ) + cos ( x - 1 ) = 2 cosx cosy ; cos ( x + y ) ...
... DIFFERENCES OF FUNCTIONS 38. From formulas ( 11 ) – ( 14 ) , we obtain Let then - sin ( x + y ) + sin ( x − y ) = 2 sin x cosy ; - sin ( x + y ) —sin ( x − y ) = 2 cosx siny ; cos ( x + y ) + cos ( x - 1 ) = 2 cosx cosy ; cos ( x + y ) ...
Página 75
... difference of ( 21 ) and ( 22 ) give cos ix = = 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 ...
... difference of ( 21 ) and ( 22 ) give cos ix = = 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 ...
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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