\(\displaystyle{\frac{{{9}\pi}}{{{4}}}}={\frac{{\pi}}{{{4}}}}+{\frac{{{8}\pi}}{{{4}}}}={\frac{{\pi}}{{{4}}}}+{2}\pi\)

so \(\displaystyle{\frac{{\pi}}{{{4}}}}\) is the reference angle \(\displaystyle\angle{45}^{{{o}}}\)

\(\displaystyle{\cos{{\left({\frac{{\pi}}{{{4}}}}\right)}}}={\frac{{\sqrt{{{2}}}}}{{{2}}}}\)

so \(\displaystyle{\frac{{\pi}}{{{4}}}}\) is the reference angle \(\displaystyle\angle{45}^{{{o}}}\)

\(\displaystyle{\cos{{\left({\frac{{\pi}}{{{4}}}}\right)}}}={\frac{{\sqrt{{{2}}}}}{{{2}}}}\)