Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical Problems |
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Page 245
... Cosine of an arc is the per- pendicular distance from the center of the circle to the sine of the arc ; or , it is the same in magnitude as the sine of the complement of the arc . Thus , CF is the cosine of the arc AB ; KB , is the sine ...
... Cosine of an arc is the per- pendicular distance from the center of the circle to the sine of the arc ; or , it is the same in magnitude as the sine of the complement of the arc . Thus , CF is the cosine of the arc AB ; KB , is the sine ...
Page 246
... cosine are each equal to radius . 2d . The sine and versed sine of a quadrant are each equal to the radius ; its cosine is zero , and its secant and tangent are infinite . 3d . The chord of an arc is twice the sine of one half the arc ...
... cosine are each equal to radius . 2d . The sine and versed sine of a quadrant are each equal to the radius ; its cosine is zero , and its secant and tangent are infinite . 3d . The chord of an arc is twice the sine of one half the arc ...
Page 248
... cosines of all arcs from 0 ° to 360 ° . Now , since all other trigo- nometrical lines can be expressed in terms of the sine and cosine , it follows that the algebraic signs of all the circular functions result from those of the sine and ...
... cosines of all arcs from 0 ° to 360 ° . Now , since all other trigo- nometrical lines can be expressed in terms of the sine and cosine , it follows that the algebraic signs of all the circular functions result from those of the sine and ...
Page 249
... cosine of two arcs , to find the sine and the cosine of the sum and of the difference of the sam arcs expressed by the sines and cosines of the separate arcs . Let G be the center of the circle , CD the greater arc , and DF the less ...
... cosine of two arcs , to find the sine and the cosine of the sum and of the difference of the sam arcs expressed by the sines and cosines of the separate arcs . Let G be the center of the circle , CD the greater arc , and DF the less ...
Page 250
... cosines , DO = sin.a ; GO : = cos.a ; FI = sin.b ; GI = cos.b. We are to find FM sin . ( a + b ) ; GM cos . ( a + b ) ; EP = = = sin . ( ab ) ; GP b ) ; GP = cos . ( a cos . ( a - b ) . Because IN is parallel to DO , the two A's , GDO ...
... cosines , DO = sin.a ; GO : = cos.a ; FI = sin.b ; GI = cos.b. We are to find FM sin . ( a + b ) ; GM cos . ( a + b ) ; EP = = = sin . ( ab ) ; GP b ) ; GP = cos . ( a cos . ( a - b ) . Because IN is parallel to DO , the two A's , GDO ...
Common terms and phrases
AB² ABCD altitude angle opposite axis bisected chord circle circumference circumscribed common cone convex surface cos.a cos.b cos.c Cosine Cotang diagonal diameter difference distance divided draw equal angles equation equiangular equivalent find the angles formulæ four magnitudes frustum given line greater half Hence the theorem homologous hypotenuse included angle inscribed intersect isosceles less Let ABC logarithm measured multiplied N.sine number of sides opposite angles parallelogram parallelopipedon pendicular perpendicular plane ST polyedron PROBLEM produced Prop proportion PROPOSITION prove pyramid quadrantal radii radius rectangle regular polygon right angles right-angled spherical triangle right-angled triangle SCHOLIUM secant segment semi-polygon similar sin.a sin.b sin.c sine solid angles sphere SPHERICAL TRIGONOMETRY straight line Tang tangent three angles three sides triangle ABC triangular prisms Trigonometry vertex vertical angle volume