Explanation:
The given equation of a wave is
\(y = 10\sin \left( {\frac{{2\pi }}{{45}}t + \alpha } \right)\)
At \(t = 0,y = 5\;cm\)
\(\therefore \quad 5=10 \sin \alpha\)
\(\Rightarrow \sin \alpha=\dfrac{1}{2}=\sin \dfrac{\pi}{6}\)
\( \Rightarrow \alpha = \frac{\pi }{6}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\)
Hence, the total phase at \(t = 7.5\;s = \frac{{15}}{2}\;s\) is \(\phi=\dfrac{2 \pi}{45} \times \dfrac{15}{2}+\dfrac{\pi}{6}=\dfrac{\pi}{2} \quad\) (using (1))