Find, in radians, the general solution of the equation cos(3x) = 0.5giving your answer in terms of pi
we have cos (3x) = 0.5 (1) we know that in the interval between [-pi; pi] there are two values that satify the equation cos(y) = 0.5 (2) the two solutions are y=pi/3 and y=-pi/3 in this interval. More generally, there are two grop of solutions which are y=(pi/3) + 2kpi and y=(-pi/3) + 2kpi (were k is a natural integer) From the equations (1) and (2) we can thus set : 3x = y <=> 3x = (pi/3) + 2k and 3x = (-pi/3) + 2k*pi so by dividing each part of the equation by 3 we get x= (pi/9) + (2k/3)*pi and x = (-pi/9) + (2k/3)*pi
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