Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic OperationsBaldwin, Cradock, and Joy, 1816 - 244 páginas |
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Página 42
... consequently be trans- formed into this : viz . COS ( AB ) COS A COS B + sin A sin B. If A and B be regarded as arcs instead of the angles which they measure , the results will be equally conclu- sive and correct . They may be expressed ...
... consequently be trans- formed into this : viz . COS ( AB ) COS A COS B + sin A sin B. If A and B be regarded as arcs instead of the angles which they measure , the results will be equally conclu- sive and correct . They may be expressed ...
Página 46
... consequently , 1 ± tan B tan ( 45 ° + B ) = ( p . ) 1 tan B If A = B , the formula ( o ) will give for the double arc , 2 tan A tan 2A = 1 - tan 2A · ( Q. ) While , on the other hand , dividing the first 1 46 Plane Trigonometry .
... consequently , 1 ± tan B tan ( 45 ° + B ) = ( p . ) 1 tan B If A = B , the formula ( o ) will give for the double arc , 2 tan A tan 2A = 1 - tan 2A · ( Q. ) While , on the other hand , dividing the first 1 46 Plane Trigonometry .
Página 53
... Consequently , from equa . ( 3 ) -b tan ( A —B ) = a + b tan ( A + B ) tana- tan 45 ° 1 + tan a tan a -a - b a + b tan † ( A — B ) . whence cot & c tan ( AB ) cotic tan ( 45 ° ) .... ( 10. ) Hence results the following practical rule ...
... Consequently , from equa . ( 3 ) -b tan ( A —B ) = a + b tan ( A + B ) tana- tan 45 ° 1 + tan a tan a -a - b a + b tan † ( A — B ) . whence cot & c tan ( AB ) cotic tan ( 45 ° ) .... ( 10. ) Hence results the following practical rule ...
Página 60
... consequently ( Euc . iii . 20 ) angle cỏв = CBA = 2 angle CAB . 2dly . Algebraically . Denote BC by x - 1 , BA by x , and Ac by x + 1 ; then , ( BE being perpendicular to AC the longest side ) we have AC : AB + BC : AB - BC AE — EC ...
... consequently ( Euc . iii . 20 ) angle cỏв = CBA = 2 angle CAB . 2dly . Algebraically . Denote BC by x - 1 , BA by x , and Ac by x + 1 ; then , ( BE being perpendicular to AC the longest side ) we have AC : AB + BC : AB - BC AE — EC ...
Página 70
... consequently ATS = 85 ° 8 ' , and OBS = 4 ° 2 ′ , whence ABS exam . 4 , is obviously applicable : so that we have 85 ° 58 ' ; to find As and AB . AS . rad3 AB.rad3 T Here method 2 , -- BT sin ATS sin ABS COSEC ( ABS - ATS ) BT sin ATS ...
... consequently ATS = 85 ° 8 ' , and OBS = 4 ° 2 ′ , whence ABS exam . 4 , is obviously applicable : so that we have 85 ° 58 ' ; to find As and AB . AS . rad3 AB.rad3 T Here method 2 , -- BT sin ATS sin ABS COSEC ( ABS - ATS ) BT sin ATS ...
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Términos y frases comunes
altitude angled spherical triangle azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian obliq oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius right angled spherical right angled triangle right ascension right line sec² secant sin A sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence zenith