Calendar: 1898-1899 Page 747

FACULTY OF SCIENCE CXV Explain clearly the meaning of sin prove that it has an infinite number of values and shew how they are related If sin-1 sin π sin-11 and cos-1 χ cos1 cos find χ and 10 Express the length of the median of triangle in terms of the sides If is the median from and χ the bisector of the angle of the triangle ABC shew that bc 2X 2X YEARS II III 11 If χ be the circular measure of an acute angle prove that χ lies between tan χ and sin Prove also that it lies between tan χ and tan 12 Obtain an expression for the length of the chain of bicycle the chain-wheels being of radii β and their centres distant χ apart If the length were given how would you proceed to find an approximate value of on the assumption that it was large compared with or 13 Prove that the product of any number of expressions of the form cos -j- sm is an expression of the same form Hence obtain cos $A in terfns of cos 14 Shew how to obtain the solution of xn by means of Trigonometry hence obtain the quadratic factors of 12- Verify your results algebraically YEAR III YEAR II may substitute any of questions 15-20 for any of questions 7-10 15 Find from the definition the differential coefficients of xn for any value of see2 χ and inx 16 If it is known that the differential coefficient of function with respect to variable is negative for particular value of the variable what may be inferred Draw diagram which may represent the graph of unc- tion which is such that the differential coefficient of the function with respect to the independent variable is always