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 |
Dentro del libro
Página 50
... natural sine and cosine of such arc . C3 C5 sin c = c + 1.2.3 1.2.3.4.5 C7 1.2.3.4.5.6.7 + & c . Cosc = 1- + 1.2 * C4 1.2.3.4 C6 ( Y. ) + & c . 1.2.3.4.5.6 These series will converge rapidly when the arc is small 50 Plane Trigonometry .
... natural sine and cosine of such arc . C3 C5 sin c = c + 1.2.3 1.2.3.4.5 C7 1.2.3.4.5.6.7 + & c . Cosc = 1- + 1.2 * C4 1.2.3.4 C6 ( Y. ) + & c . 1.2.3.4.5.6 These series will converge rapidly when the arc is small 50 Plane Trigonometry .
Página 54
... cosc , COS C = 2ab These equations are , obviously , equivalent to prop . 17 , chap . ii . They may be expressed in a form rather better suited to computation , thus : COS A = - a ) ( b + c + a ) ( b + c — 2bc - 1 .... ( 12. ) Where ...
... cosc , COS C = 2ab These equations are , obviously , equivalent to prop . 17 , chap . ii . They may be expressed in a form rather better suited to computation , thus : COS A = - a ) ( b + c + a ) ( b + c — 2bc - 1 .... ( 12. ) Where ...
Página 221
... cases , cos = √ ( 1 − sin2 ) , we have cos 6 cosc √ [ ( 1 sin2 ) ( 1 - sin2 c ) ] ; we have also , as above , sin be , and sin cfr . = - = Substituting these values in the equation 1 of the pre- Geodesic Operations . 221.
... cases , cos = √ ( 1 − sin2 ) , we have cos 6 cosc √ [ ( 1 sin2 ) ( 1 - sin2 c ) ] ; we have also , as above , sin be , and sin cfr . = - = Substituting these values in the equation 1 of the pre- Geodesic Operations . 221.
Página 222
... cosc + sin ? c ; and thence 1-2 sin A ' ( 1-2 sin2 A ) cos2c + ( 1 cos2 ( c ) : from which may be deduced = sin A sina cos c . ( 3. ) : Cor . 2. Also , since.cos c .... - ✓ ( 1 sinc ) = √ ( L - - y2 ) , equa . 2 will , in this case ...
... cosc + sin ? c ; and thence 1-2 sin A ' ( 1-2 sin2 A ) cos2c + ( 1 cos2 ( c ) : from which may be deduced = sin A sina cos c . ( 3. ) : Cor . 2. Also , since.cos c .... - ✓ ( 1 sinc ) = √ ( L - - y2 ) , equa . 2 will , in this case ...
Otras ediciones - Ver todas
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