...when n is indefinitely diminished is the circular measure of an angle of one minute; and so on. 120. If 6 be the circular measure of a positive angle less than SP a right angle, sin 6 is greater than 6 — -r . ft ft ft ft For sin 6 = 2 sin <r cos ^ ; and tan...

...sin 6 (16 cos1 о - 16 cos' ö + 3 cos 6). TT IX. CONSTRUCTION OF TKIGONOMETKICAL TABLES. 116. If в be the circular measure of a positive angle less than a right angle, в is greater than sin в and less than tan 0. Let АО В be an angle less than a right angle and...

...spherical right triangle may be solved. 4. Prove any one of Napier's analogies. 5. Prove that if Q be the circular measure of a positive angle less than a right angle the limit of the ratio sinO: 0. when 6 is indefinitely diminished, is unity ; but if degree measure...

...Solve the equations — (i) cos 0 — cos 20 = sin '60 (ii) sin 0 — cos 0 = 4 sin 0 cos2 0 2. If 0 be the circular measure of a positive angle less than a right angle, 0 is greater than sin 0 and less than tan 0. Hence show that when 0 is very small, sin 0=0, and tan...

...11. n - 15, r = 6. Higher Mathematics. TRIGONOMETRY ; STATICS ; HYDROSTATICS. Junior and Senior. 1 . If 6 be the circular measure of a positive angle less than 90°, prove (i) 0 is greater than sin 0, and less than tan 0 ; (ii) 8^-- ^= 1 when 0 is very small....

...6 sm?t° \ 180 6 \ , ... 180 = — . — — ^ ) , when n = 0, ts . IT SHI 6) n 292. To prove that if 6 be the circular measure of a positive angle less than a right angle, sin 6 lies between 6 and It has been proved that sin 6 is less than 6 ......... (i). And that 6 is...

...factors. 4. Shew that cot {0 + tan-1 (tans0)} = 2 cot 0. 5. Prove that sin 0 > d — — , 6 being the circular measure of a positive angle less than a right angle. 6. Find the radii of the inscribed and circumscribed circles of a regular polygon, that is of a polygon...

...positive and unequal, prove that (a + b + c+ ...+k\ n . . , , ,, I - 1 1s greater than (abc. ,.k). 7. If 0 be the circular measure of a positive angle less than a right angle, prove that sin 0 is greater than 0 -- ; and that cos 0 is less than ffi 0* I -- +-j2 16 03 Given —...

...each parallel to one asymptote and terminated by the other, prove that . Oy = CA* + CB*. II. — 1 . If 6 be the circular measure of a positive angle less than a right angle, prove that sin 0 is greater than 6 — — and that cos 6 is greater 4 al than 1 _ " '0 2. Prove that...

...magnitude between the greatest and least of the aforesaid fractions. III. — 1. Prove that if 6 he the circular measure of a positive angle less than a right angle sin 6 lies between 6 and 6 — - 03. 4 2. Apply Demoivre's theorem to express cos nO and sin nO in...