Calendar: 1891-1892 Page 816

cxxviii ENGINEERING DEPARTMENT Shew that if θ be the circular measure of an angle less sin θ θ than right angle then -- are both less than unity θ tan θ and decrease as θ increases From given circle segment is cut off greater than semicircle Shew that the greater the chord of this segment the less is the whole perimeter Write down the expansion of 10ge in ascending powers of Shew that if χ is greater than χ χ Sx3 bx and deduce log V2 '2006706 Shew that xn vanishes when χ cos si η Deduce the real factors of this expression AVrite down the exponential values of sin χ and cos and prove from them sin β sin cos β cos sin β SECOND AND THIRD YEARS £0gant$n14 anfc flfUnguratioii Explain the meaning of logarithm If log express χ in terms ofy As an example sup- pose χ 125 Explain how it is that tables of logarithms enable us to replace multiplication and division by addition and sub- traction Given log 13 1139434 log 12304489" Find 10-2-21 and log 307692 Calculate by means of the tables 49-2061 χ 00495534 4-90996 Also calculate it roughly to figure without the tables