Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 21
Page 214
... formula cos A = sin ( 90 ° -A ) ; or if we require it , by means of the formula cos A = sin ( 90 ° + A ) : and thus , if we can find the value of the sines in all possible cases , we can also find that of the cosines . Besides , as has ...
... formula cos A = sin ( 90 ° -A ) ; or if we require it , by means of the formula cos A = sin ( 90 ° + A ) : and thus , if we can find the value of the sines in all possible cases , we can also find that of the cosines . Besides , as has ...
Page 215
... formulas , which we now proceed to explain . THEOREMS AND FORMULAS RELATING TO SINES , COSINES , TANGENTS , & c . XV . The sine of an arc is half the chord which subtends a double arc . For the radius CA , perpen- dicular to the chord ...
... formulas , which we now proceed to explain . THEOREMS AND FORMULAS RELATING TO SINES , COSINES , TANGENTS , & c . XV . The sine of an arc is half the chord which subtends a double arc . For the radius CA , perpen- dicular to the chord ...
Page 216
... formulas required . It may also be observed , that the two last formulas might be deduced from the first two , by simply putting 90 ° -A instead of A. From these formulas , may be deduced the values , with their proper signs , of the ...
... formulas required . It may also be observed , that the two last formulas might be deduced from the first two , by simply putting 90 ° -A instead of A. From these formulas , may be deduced the values , with their proper signs , of the ...
Page 217
... formulas , that the secant has always the same algebraic sign as the cosine , and the co- secant the same as the sine . Hence , the secant is positive on the right of the vertical diameter DE , and negative on the left of it ; the ...
... formulas , that the secant has always the same algebraic sign as the cosine , and the co- secant the same as the sine . Hence , the secant is positive on the right of the vertical diameter DE , and negative on the left of it ; the ...
Page 218
... formula cot Axtang A = R2 might be deduced imme- diately , by comparing the similar triangles CAT , CDS , which give AT : CA ... formulas ; but they may be found directly by the same figure . For , produce the sine DI till it meets the ...
... formula cot Axtang A = R2 might be deduced imme- diately , by comparing the similar triangles CAT , CDS , which give AT : CA ... formulas ; but they may be found directly by the same figure . For , produce the sine DI till it meets the ...
Other editions - View all
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