When $\displaystyle{x}={0}\usepackage{cmbright}\Huge\$ :

$\displaystyle{y}={a}{\sin{{b}}}{x}={a}{\sin{{\left({b}\cdot{0}\right)}}}={a}{\sin{{0}}}={a}\cdot{0}={0}\usepackage{cmbright}\Huge\$ , and

$\displaystyle{y}={a}{\cos{{b}}}{x}={a}{\cos{{\left({b}\cdot{0}\right)}}}={a}{\cos{{0}}}={a}\cdot{1}={a}\ne{0}\usepackage{cmbright}\Huge\$

So the graph of $\displaystyle{y}={a}{\sin{{b}}}{x}\usepackage{cmbright}\Huge\$ must pass through $\displaystyle{\left({0},{0}\right)}\usepackage{cmbright}\Huge\$ and the graph of $\displaystyle{y}={a}{\cos{{b}}}{x}\usepackage{cmbright}\Huge\$ will not pass through $\displaystyle{\left({0},{0}\right)}\usepackage{cmbright}\Huge\$ , regardless of the values of a and b.