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 86
... obvious transforma tions , the six usual cases of right angled spherical tri- angles may be solved , as below . Case I. 26. Given the hypothenuse a and an angle 6 86 Spherical Trigonometry . Right angled spherical triangles.
... obvious transforma tions , the six usual cases of right angled spherical tri- angles may be solved , as below . Case I. 26. Given the hypothenuse a and an angle 6 86 Spherical Trigonometry . Right angled spherical triangles.
Página 87
... hypothenuse a and an angle B ; sin b or , sin side req . X sin hypoth . to find the rest ; sin a sin B ; sin opp . angle B tan ctan a cos B ; C G or , tan side req . = tan hypoth . x cos included angle , cot c = cos a tan B ; or , cot ...
... hypothenuse a and an angle B ; sin b or , sin side req . X sin hypoth . to find the rest ; sin a sin B ; sin opp . angle B tan ctan a cos B ; C G or , tan side req . = tan hypoth . x cos included angle , cot c = cos a tan B ; or , cot ...
Página 91
... hypothenuse and 4 one leg of a right angled triangle . The above transformation , therefore , is equivalent to the division of the proposed triangle into two , by an arc from the vertical angle a falling perpendicularly upon the oppo ...
... hypothenuse and 4 one leg of a right angled triangle . The above transformation , therefore , is equivalent to the division of the proposed triangle into two , by an arc from the vertical angle a falling perpendicularly upon the oppo ...
Página 99
... hypothenuse a , and the other two sides 6 and c : that is , 90 ° - a , 90 ° B , 90 ° - c , b , and c , are the five circular parts . Any one of these five may be called a middle part ; then the two parts next adjacent , one on the right ...
... hypothenuse a , and the other two sides 6 and c : that is , 90 ° - a , 90 ° B , 90 ° - c , b , and c , are the five circular parts . Any one of these five may be called a middle part ; then the two parts next adjacent , one on the right ...
Página 112
... hypothenuse a 64 ° 40 ' , and one leg b = 42 ° 12 ′ . Required the rest . This example falls under case 2 , section 2 , of the preceding chapter , where sin в , a req . angle sin given side sin hypoth . COS C , the side req . = cos ...
... hypothenuse a 64 ° 40 ' , and one leg b = 42 ° 12 ′ . Required the rest . This example falls under case 2 , section 2 , of the preceding chapter , where sin в , a req . angle sin given side sin hypoth . COS C , the side req . = cos ...
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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