When $x=\frac{A}{2}, \Rightarrow \frac{A}{2}=A \cos \left(\omega t+\phi_{1}\right)$

or $60^{\circ}=\omega t+\phi_{1} \ldots . .(1)$

When $x=-\frac{A}{\sqrt{2}}, \Rightarrow-\frac{A}{\sqrt{2}}=A \cos \left(\omega t+\phi_{1}\right)$

or $225^{\circ}=\omega t+\phi_{2} \ldots . .(2)$

$(2)-(1) \Rightarrow \phi_{2}-\phi_{1}=225-60=165^{\circ}$

also $x=A \sin (\omega t+\phi)$

When $x=\frac{A}{2}, \Rightarrow \frac{A}{2}=A \sin \left(\omega t+\phi_{1}\right)$

or $30^{\circ}=\omega t+\phi_{1} \ldots . .(1)$

When $x=-\frac{A}{\sqrt{2}}, \Rightarrow-\frac{A}{\sqrt{2}}=A \sin \left(\omega t+\phi_{1}\right)$

or $225^{\circ}=\omega t+\phi_{2} \ldots . .(2)$

$(2)-(1) \Rightarrow \phi_{2}-\phi_{1}=225-30=195^{\circ}$