Elements of Geometry and Trigonometry |
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Page 213
... Cosine 1q + 2q 3q 4q Tangent Cotangent + + ++ XIII . In trigonometry , the sines , cosines , & c . of arcs or an- gles greater than 180 ° do not require to be considered ; the angles of triangles , rectilineal as well as spherical , and ...
... Cosine 1q + 2q 3q 4q Tangent Cotangent + + ++ XIII . In trigonometry , the sines , cosines , & c . of arcs or an- gles greater than 180 ° do not require to be considered ; the angles of triangles , rectilineal as well as spherical , and ...
Page 214
... cosine , tan- gent , & c . S ' D S M MT P ' P B A N R V E Hence it appears , that whatever be the magnitude of x the ... cosine , while those whose extremities fall on the left have a negative cosine . Thus from 0 ° to 90 ° the cosines ...
... cosine , tan- gent , & c . S ' D S M MT P ' P B A N R V E Hence it appears , that whatever be the magnitude of x the ... cosine , while those whose extremities fall on the left have a negative cosine . Thus from 0 ° to 90 ° the cosines ...
Page 215
... cosines of the various arcs which are multiples of the quadrant have the following values : sin 0 ° = 0 sin 90 ° sin 180 ° = 0 R sin 270 ° -R sin 360 ° = 0 sin 450 ° = R , sin 540 ° = 0 sin 630 ° -R sin 720 ° = 0 sin 810 ° R & c . & c ...
... cosines of the various arcs which are multiples of the quadrant have the following values : sin 0 ° = 0 sin 90 ° sin 180 ° = 0 R sin 270 ° -R sin 360 ° = 0 sin 450 ° = R , sin 540 ° = 0 sin 630 ° -R sin 720 ° = 0 sin 810 ° R & c . & c ...
Page 216
... cosines CP , CP ' , are equal and have contrary signs ; and the same cosine CP answers to the two arcs AM , AN , whose signs MP , PN , are also equal , and have contrary signs . Thus , for example , having found sin 30 ° = R , we may de ...
... cosines CP , CP ' , are equal and have contrary signs ; and the same cosine CP answers to the two arcs AM , AN , whose signs MP , PN , are also equal , and have contrary signs . Thus , for example , having found sin 30 ° = R , we may de ...
Page 217
... cosine have like algebraic signs , and both negative , when the sine and cosine have contrary algebraic signs . Hence , the tangent and cotangent have the same sign in the diagonal quadrants : that is , positive in the 1st and 3d , and ...
... cosine have like algebraic signs , and both negative , when the sine and cosine have contrary algebraic signs . Hence , the tangent and cotangent have the same sign in the diagonal quadrants : that is , positive in the 1st and 3d , and ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex