Elements of Geometry and Trigonometry |
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Page 213
... Sine Cosine Tangent Cotangent 1q + 2q + + 3q + 4q 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 ...
... Sine Cosine Tangent Cotangent 1q + 2q + + 3q + 4q 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 ...
Page 214
... sine may always be expressed , with a proper sign , by the sine of an arc less than 180 ° . For , in the first place , we may subtract 360 ° from the arc x as often as they are contained in it ; and y being the remainder , we shall have ...
... sine may always be expressed , with a proper sign , by the sine of an arc less than 180 ° . For , in the first place , we may subtract 360 ° from the arc x as often as they are contained in it ; and y being the remainder , we shall have ...
Page 215
... sine of an arc is half the chord which subtends a double arc . For the radius CA , perpen- dicular to the chord MN , bi- sects this chord , and likewise the arc MAN ; hence MP , the sine of the arc MA , is half the chord MN which ...
... sine of an arc is half the chord which subtends a double arc . For the radius CA , perpen- dicular to the chord MN , bi- sects this chord , and likewise the arc MAN ; hence MP , the sine of the arc MA , is half the chord MN which ...
Page 216
... sine of an arc is given , its co- sine may be found , and re- ciprocally , by means of the B M T P ' P A 19 R E formulas cos A = ± √ ( R2 — sin2A ) , and sin A = ± √ ( R2 — cos2A ) . The sign of these formulas is + , or because the same ...
... sine of an arc is given , its co- sine may be found , and re- ciprocally , by means of the B M T P ' P A 19 R E formulas cos A = ± √ ( R2 — sin2A ) , and sin A = ± √ ( R2 — cos2A ) . The sign of these formulas is + , or because the same ...
Page 217
... sine 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 ...
... sine 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 ...
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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 consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides 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 solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex