EXAMPLES II 37 



(10) Write down the values of sin 101 20', cos 198 82', tan 

 278 48', sin 886 22', cos 557 53', tan 785 89', sin ( - 221 17'), 

 cos ( - 86 19'), and tan ( - 894 49'). 



(11) If x = r(l - cos 0) +^ (1 - cos 26) and r = 1, I = 5. Cal- 

 culate the values of x when has the values 0, 30, 60, 90, 

 120, 150, and 180. 



(12) If y = e? 8in 6 and a = 2, calculate the values of y when 6 



has the values J ^> J> 0, - - r* - 5' Plot y and 6 on squared 

 2 o o 9 



paper, and use your graph to solve the equation e 2 8ln * = 2. 

 Verify your result by calculation. 



(18) Put 9 sin + 13 cos in the form A sin (0 + a), giving 

 the values of A and a. From the result find the value of which 

 causes the expression to vanish. 



(14) Put 21 cos 0-16 sin in the form A cos (0 + a), giving 

 the values of A and a. From the result find the greatest and least 

 values of the expression and the values of producing them. 



Solve the equations : 



(15) 3 sin + 7 cos = 7-5. 



(16) 8 sin + 12 cos = - 14-1. 



(17) 13 cos - 8 sin = 15. 



(18) 11 cos - 15 sin = - 18. 



(19) 35 cos - 12 sin = - 37. 



(20) 5 sin + 12 cos = 13. 



(21) 8 sin + 11 cos = 0. 



(22) If tan A = - without using the tables find the trigono- 



m 



^ 



metrical ratios of the angles 2A, and 3A. 





 n 



(23) If x = tan - show that a sin + b cos = c can be put 



m 



in the form 2ax + 6(1 x 2 ) = c(l + x z ), and hence solve the equa- 

 tion 9 sin + 13 cos = 15. 



(24) From a circular disc of metal 8" radius, a sector whose 

 angle is 54 is cut away, and the remainder is formed into a conical 

 vessel. Find the volume of that vessel. 



Solve the equations, keeping r always positive : 



(25) r cos = 6, r sin = 11. 



(26) r cos = - 5, r sin = 13. 



(27) r cos = - 10, r sin = - 15. 



(28) r cos = 12, r sin = - 7. 



