x=theta
so we know that tanx = sinx/cosx
therefore is tanx = 4/3 and sinx = -4/5
we can set up an equation to find cosx
so 4/3 = (-4/5)/cosx
we can multiply x to have cosx(4/3)=-4/5
we can then divide 4/3 over so we have
cosx = (-4/5)/(4/3)
therefore, cos x = -3/5
there is the answer
i hope this help