...investigation depends on four fundamental propositions, which may be deduced as follows :— PEOPOSITION 1. The sine of the sum of two angles is equal to the sine of the first into the cosine of the second, together with the cosine of the first into the sine...

...quarters the sine and cosine are negative. 2. Express each formula in ordinary language ; for example : the sine of the sum of two angles is equal to the sum of the products of . the sine of each by the cosine of the other. 3. Demonstrate cos. 12° = J...

...in (3), and denoting the formula by (a), we have (a) sin (a + b) = sin a cos b + cos a sin b. Hence, The sine of the sum of two angles is equal to the yine of tíie first into the co-sine of the second, plns the cosine of the first into the sine of the...

...(2), (3), and (4), in (1), we have, (6) cos (a + 6) = cos a cos b — sin a sin b. Hence, The co-sine of the sum of two angles is equal to the product of their co-sines minus the product of their sines. 90. Problems. 1. Prove that formulas (a) and (6) become...

...(a), and reducing, we have cot a cot b — 1 (/) cot (a + 5) = cot a -1- cot b Hence, The co-tangent of the sum of two angles is equal to the product of their co-tangents, minus 1, dirided by the sum of their co-tangents. Dividing (c) by (d), and reducing,...

...the first by the sine of the second ; ie, sin (a — /3) = sin a cos (3 — cos a sin |3. The cosine of the sum of two angles is equal to the product of their cosines, minus the product of their sines ; ie, cos (a -f- /3) = cos a cos f3 — sin a sin /3....

..._ — _ -1 V"2' 2 "2 ' 2 " = -25882. 2 s/2 From the foregoing remarks we have seen that : — 1st. The sine of the sum of two angles is equal to the sine of the first into the cosine of the second, together with the cosine of the first into the sine...

..., sin x sin y subst1tut1ng tan x and tan y for - and - — . cos x cos y THEOREM VI. The cotangent of the sum of two angles is equal to the product of their cotangents minus 1, divided by tlie sum of their cotangents. For, cos (x + y) cos x cos y —...

...each of the following: sin 75°, cos 240°, cos 105°, tan 330°, esc 15 . 4 Prove that the cosine of the sum of two angles is equal to the product of the cosines of the angles less the product of their sines. 5 Find the value of the sine of 4 A and of the...

...important that they should be carefully memorized. They may be translated into words as follows : I. The sine of the sum of two angles is equal to the sine of the first into the cosine of the second, plus the cosine of the first into the sine of the...