the number of integral values of k for which the equation 7cosx+5sinx=2k+1 has a solution is ( show the steps)

7cosx+5sinx lies between +-sqrt(49+25)= +-(74) which is appprox 8.6

hence 2k+1 must lie between -8.6 and 8.6 or 2k must lie between -9.6 and 7.6 and k must lie between -4.8 and 3.8 

therefore integral values of k possible are -4 -3 -2 -1 0 1 2 3 ie 8 values