60 PRACTICAL MATHEMATICS 



EXAMPLES IV 



Find the result of operating with each of the following complex 

 quantities on sin qt : 



(15) If x = 0-82, find sinh x, cosh x, and tanh x. 



(16) If sinh x = 0-65, find x. 



(17) If cosh x = 2-25, find x. 



(18) If tanh x = 0-75, find x. 



(19) Express cosh - and sinh J-i each in the form a + W, 



^ o 



giving the values of a and 6 correct to four significant figures. 



-- 



(20) If sinh = i, find 8 in terms of x. 



X -4- 8 



(21) If cosh = -3_, find in terms of x. 



2V7 



(22) In a telephone line of length /, where q is 2nf, if / is fre- 

 quency or pitch of a musical note ; let r, the resistance per mile, 

 be 88 ; let k, the capacity per mile, be 5 x 10~ 8 . Take q = 5000. 

 Let n = Vrkqi where i means V 1. Let Z = 40 miles. If 

 R = 100 + 0-04^ be the resistance of the receiving telephone, the 



2V 



current through it is C = - - 2-r where V is 10 sin 50002. 



C is of the form a sin (qt + b) where q is 5000, find a and b. 



(B. of E., 1912.) 

 Express each of the following functions in terms of the sines 



or cosines of multiple angles : 



(23) sin 3 (24) sin 6 6 



(25) cos 5 (26) cos 6 



(27) sin 3 cos 3 (28) sin 4 cos 4 



(29) sin 3 cos 5 (30) sin 4 cos 2 



