Question

# Write the function y=-sin x as a phase shift of y=sin x.

Analyzing functions
Write the function $$\displaystyle{y}=-{\sin{{x}}}$$ as a phase shift of $$\displaystyle{y}={\sin{{x}}}$$.

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