For a function \(\displaystyle{y}={\sin{{\left({x}+{a}\right)}}}\), a is a phase shift.

So \(\displaystyle{y}=-{\sin{{x}}}\)

\(\displaystyle{y}={\sin{{\left({x}+\pi\right)}}}\)

As the sine function is negative at \(\displaystyle{180}+θ\), the phase shift is \(\displaystyle\pi\)

\(\displaystyle{y}={\sin{{\left({x}+\pi\right)}}}\)

So \(\displaystyle{y}=-{\sin{{x}}}\)

\(\displaystyle{y}={\sin{{\left({x}+\pi\right)}}}\)

As the sine function is negative at \(\displaystyle{180}+θ\), the phase shift is \(\displaystyle\pi\)

\(\displaystyle{y}={\sin{{\left({x}+\pi\right)}}}\)