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 31
... taken from half the sum , leaves the less * .- All the angles becoming known by this process , the third side is found by the rule in case 1 . Example I. 8. Let there be given in a plane triangle ABC , AC 450 , BC = 540 , and the ...
... taken from half the sum , leaves the less * .- All the angles becoming known by this process , the third side is found by the rule in case 1 . Example I. 8. Let there be given in a plane triangle ABC , AC 450 , BC = 540 , and the ...
Página 38
... taken negatively , its sine would , for like reasons , be negative in the first half , positive in the second half , of the circle . 4. The cosine of an arc is equal to radius at the point A , where the arc is evanescent . From thence ...
... taken negatively , its sine would , for like reasons , be negative in the first half , positive in the second half , of the circle . 4. The cosine of an arc is equal to radius at the point A , where the arc is evanescent . From thence ...
Página 49
... taken , we shall have ( cos Asin A 1 ) cos 2A sin 2A - 1 ; if three factors be taken , the result , will be ( cos Asin A - 1 ) 3 = cos 3A + sin 3A −1 , Whence , in general , ( COS Asin A − 1 ) ” cos na sin na √ .1 . 30. From the last ...
... taken , we shall have ( cos Asin A 1 ) cos 2A sin 2A - 1 ; if three factors be taken , the result , will be ( cos Asin A - 1 ) 3 = cos 3A + sin 3A −1 , Whence , in general , ( COS Asin A − 1 ) ” cos na sin na √ .1 . 30. From the last ...
Página 53
... multiplied by a , the second by b , the third by c , and each of the equa- tions thus obtained , being taken from the sum of the other two , there will arise · b2 + c2 — a2 = 2bc cos A Analytical Investigation of Properties . 53.
... multiplied by a , the second by b , the third by c , and each of the equa- tions thus obtained , being taken from the sum of the other two , there will arise · b2 + c2 — a2 = 2bc cos A Analytical Investigation of Properties . 53.
Página 57
... taken make equal sums , it is highly probable they are all correct . Taking these from Dr. Hutton's tables , we have sin 9 ° 1564345 sin 27 ° = • 4539905 .sin 45 ° • 7071068 sin 81 ° = • 9876883 sin 63 ° = 8910065 1.5981133 .... equal ...
... taken make equal sums , it is highly probable they are all correct . Taking these from Dr. Hutton's tables , we have sin 9 ° 1564345 sin 27 ° = • 4539905 .sin 45 ° • 7071068 sin 81 ° = • 9876883 sin 63 ° = 8910065 1.5981133 .... equal ...
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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