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 8
... tan2 ) . 5. tan = 7. sec = rad ' x sin COS rad2 COS • These , when unity is circle , become - 1. cos = √ ( 1 − sin2 ) . 3. sec = ( 1 + tan2 ) . 5. tan = sin COS • 6. cot = COS sin 2. tan = √ ( sec2 — rad2 ) . 4. cosec√ ( rad2 + cot2 ) ...
... tan2 ) . 5. tan = 7. sec = rad ' x sin COS rad2 COS • These , when unity is circle , become - 1. cos = √ ( 1 − sin2 ) . 3. sec = ( 1 + tan2 ) . 5. tan = sin COS • 6. cot = COS sin 2. tan = √ ( sec2 — rad2 ) . 4. cosec√ ( rad2 + cot2 ) ...
Página 23
... 89 ° 59 ' cos I ' sin 2 ' tan 2 ' = = cot 89 ° 58 ' cos 2 ' & c . & c . & c . Above 45 ° the process may be considerably simplified by the theorem for the tangents of the sums and General Properties of Lines and Angles . 23.
... 89 ° 59 ' cos I ' sin 2 ' tan 2 ' = = cot 89 ° 58 ' cos 2 ' & c . & c . & c . Above 45 ° the process may be considerably simplified by the theorem for the tangents of the sums and General Properties of Lines and Angles . 23.
Página 48
... tan2 ( 45 ° + B ) ; 1 + cos A -COS A - sin B 1 - СОЗ В sin2 ( 45 ° + B ) 1 Cos2 A = cot2 LA sino ( 450 — ¿ B ) - sin1B 28. Some useful theorems in the computation of sines , cosines , & c . result from the introduction of the imagi ...
... tan2 ( 45 ° + B ) ; 1 + cos A -COS A - sin B 1 - СОЗ В sin2 ( 45 ° + B ) 1 Cos2 A = cot2 LA sino ( 450 — ¿ B ) - sin1B 28. Some useful theorems in the computation of sines , cosines , & c . result from the introduction of the imagi ...
Página 56
... ( tan2 + rad2 ) , we have 2 Bec 15 ° ( 2— √3 ) 2 + 12 = √8—4√3 = √6 − √2 . sec 75 ° = √ ( 2 + √3 ) 2 + 12 = √ 8 + 4√3 = √6 + √2 . sec 2210 = √ ( √2 −1 ) 2 + 12 = √4-2√2 . 2 --- sec 673 ° = √ ( √2 + 1 ) 2 + 12 = ...
... ( tan2 + rad2 ) , we have 2 Bec 15 ° ( 2— √3 ) 2 + 12 = √8—4√3 = √6 − √2 . sec 75 ° = √ ( 2 + √3 ) 2 + 12 = √ 8 + 4√3 = √6 + √2 . sec 2210 = √ ( √2 −1 ) 2 + 12 = √4-2√2 . 2 --- sec 673 ° = √ ( √2 + 1 ) 2 + 12 = ...
Página 90
... tan2 A 1 cos ( bc ) cos a cos a - - cos ( b + c ) • Whence , from the 4th of equa . ( u ) chap . iv . sin ( a + b ― c ) sin ( a + e- tan2 A = • sin ( a + b + c ) sin ( b + c − a ) Hence we have , for the tangents of the half angles ...
... tan2 A 1 cos ( bc ) cos a cos a - - cos ( b + c ) • Whence , from the 4th of equa . ( u ) chap . iv . sin ( a + b ― c ) sin ( a + e- tan2 A = • sin ( a + b + c ) sin ( b + c − a ) Hence we have , for the tangents of the half angles ...
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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