Question 300382
{{{4sin(4t) + 3cos(4t) = 0}}}
{{{4sin(4t) =-3cos(4t)}}}
{{{sin(4t)/cos(4t)=-3/4}}}
{{{tan(4t)=-3/4}}}
{{{4t=arctan(-3/4)+ pi}}} 
{{{t=arctan(-3/4)/4 + pi/4}}}
You can also bring out the negative sign from the arctan argument since
{{{tan(-x)=-tan(x)}}}

{{{t=-arctan(3/4)/4 + pi/4}}}
{{{t=pi/4-arctan(3/4)/4 }}}