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 23
... cos 2 ' sin 30 ° 3 ' cos 3 ′ · -D sin 29 ° 58 ′ sin 29 ° 57 ' . And these being continued to 60 ° , the cosines also become known to 60 ° ; because cos 30 ° 1 ' = sin 59 ° 59 ' cos 30 ° 2 ′ = sin 59 ° 58 ' . The sines and cosines from ...
... cos 2 ' sin 30 ° 3 ' cos 3 ′ · -D sin 29 ° 58 ′ sin 29 ° 57 ' . And these being continued to 60 ° , the cosines also become known to 60 ° ; because cos 30 ° 1 ' = sin 59 ° 59 ' cos 30 ° 2 ′ = sin 59 ° 58 ' . The sines and cosines from ...
Página 45
... cos2 2A = 1 . Hence x4 ..x2 = - x2 + 1 = { ( 1 - cos2 2A ) = sin2 24 , sin 2A , and x = sin 2A , and ≈ = √ ( 1 ± sin 2a ) √ ( 1 sin 2a ) . 3 sin 2A ) . COS § √ ( 1 - A ) Hence , sin A = -- ( 1 + sin 2A ) — ¦ √ ( 1 − sin 24 cos A1 ...
... cos2 2A = 1 . Hence x4 ..x2 = - x2 + 1 = { ( 1 - cos2 2A ) = sin2 24 , sin 2A , and x = sin 2A , and ≈ = √ ( 1 ± sin 2a ) √ ( 1 sin 2a ) . 3 sin 2A ) . COS § √ ( 1 - A ) Hence , sin A = -- ( 1 + sin 2A ) — ¦ √ ( 1 − sin 24 cos A1 ...
Página 46
... cos2 A = 1 + cos A , and 2 sin2 bac ..cos & a = or cos 1+ COS A 2995 - ; sin A 3 ) } a = { √ ( 2 + 2 cos a ) sinA = √ ( 2 2 cos A ) A = 1 - 3.90s br - 2 cos 2A . cos A , COS A ( N. ) Suppose , for example , A 60 ° , then cos a = sin ...
... cos2 A = 1 + cos A , and 2 sin2 bac ..cos & a = or cos 1+ COS A 2995 - ; sin A 3 ) } a = { √ ( 2 + 2 cos a ) sinA = √ ( 2 2 cos A ) A = 1 - 3.90s br - 2 cos 2A . cos A , COS A ( N. ) Suppose , for example , A 60 ° , then cos a = sin ...
Página 48
... cos2 A sin A + sin B COS ACOS B sin A + sin B COS B COS A COS A + COSB COS A - COS B 1 + sin B 1 - sin B - 1 + sin B ... Cos2 A = cot2 LA sino ( 450 — ¿ B ) - sin1B 28. Some useful theorems in the computation of sines , cosines , & c ...
... cos2 A sin A + sin B COS ACOS B sin A + sin B COS B COS A COS A + COSB COS A - COS B 1 + sin B 1 - sin B - 1 + sin B ... Cos2 A = cot2 LA sino ( 450 — ¿ B ) - sin1B 28. Some useful theorems in the computation of sines , cosines , & c ...
Página 50
... COS2 A = ) , sin 2 = 2 A n n2 ? - - C3 n3 , A , cos 3A , will each 1. The two last formulæ will , therefore , be reduced to the following , by means of which it will be easy to express the sine and cosine of any arc , in parts of that ...
... COS2 A = ) , sin 2 = 2 A n n2 ? - - C3 n3 , A , cos 3A , will each 1. The two last formulæ will , therefore , be reduced to the following , by means of which it will be easy to express the sine and cosine of any arc , in parts of that ...
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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