The graph of cosine has a repeating hill and valley pattern. The pattern repeats after intervals of length $\displaystyle{2}\pi\usepackage{cmbright}\Huge\$ in both directions. In particular:

$\displaystyle\frac{\sqrt{{2}}}{{2}}={\cos{{\left(\frac{{{7}\pi}}{{4}}\right)}}}={\cos{{\left(\frac{{{7}\pi}}{{4}}-{2}\pi\right)}}}={\cos{{\left(-\frac{\pi}{{4}}\right)}}}\usepackage{cmbright}\Huge\$

Therefore, the point $\displaystyle{\left(-\frac{\pi}{{4}},\frac{\sqrt{{2}}}{{2}}\right)}\usepackage{cmbright}\Huge\$ is on the graph of cosine. Because $\displaystyle{y}={\cos{\theta}}\usepackage{cmbright}\Huge\$ is symmetric about the y-axis, the point $\displaystyle{\left(\frac{\pi}{{4}},\frac{\sqrt{{2}}}{{2}}\right)}\usepackage{cmbright}\Huge\$ is also on the graph.