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 37
... the sine diminishes , but is to be regarded as positive till the are becomes AEA ' or 180 ° . In that state of the arc the value of the sine is obviously 0. Passing on to the third quadrant , Analytical Plane Trigonometry . 37.
... the sine diminishes , but is to be regarded as positive till the are becomes AEA ' or 180 ° . In that state of the arc the value of the sine is obviously 0. Passing on to the third quadrant , Analytical Plane Trigonometry . 37.
Página 38
... positive in the fifth quadrant ; as it obvi- ously ought to do , since the fifth quadrant is coincident with the first . In the 1st and 2d quadrants , then , the sines are + , In the 3d and 4th , they are - . If the arc were taken ...
... positive in the fifth quadrant ; as it obvi- ously ought to do , since the fifth quadrant is coincident with the first . In the 1st and 2d quadrants , then , the sines are + , In the 3d and 4th , they are - . If the arc were taken ...
Página 39
... positive . The tangent , therefore , changes its sign at the end of every quadrant , where it passes alternately through nothing and infinity ; these being , indeed , the algebraic indications of the changes of sign . If the arc is ...
... positive . The tangent , therefore , changes its sign at the end of every quadrant , where it passes alternately through nothing and infinity ; these being , indeed , the algebraic indications of the changes of sign . If the arc is ...
Página 40
... positive quantity added . By letting fall perpendiculars from the angles A and B , upon the opposite sides , or their continuations , precisely analo- gous results will be obtained . They may be placed to- gether , thus a = b cos c + c ...
... positive quantity added . By letting fall perpendiculars from the angles A and B , upon the opposite sides , or their continuations , precisely analo- gous results will be obtained . They may be placed to- gether , thus a = b cos c + c ...
Página 94
... positive . The expressions for the tangents and cosines are omitted , to save room , 2. Given A , B , c ; to find c . Here , by applying in like manner , the equations ( 12 ) , ( 13 ) , to the supplemental triangle , we shall have cot ...
... positive . The expressions for the tangents and cosines are omitted , to save room , 2. Given A , B , c ; to find c . Here , by applying in like manner , the equations ( 12 ) , ( 13 ) , to the supplemental triangle , we shall have cot ...
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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