Given

\(\displaystyle{\sin{{t}}}={\frac{{{4}}}{{{5}}}}\)

We need to find a value of

\(\displaystyle{\sin{{\left({t}+\pi\right)}}}\)

Remember that

\(\displaystyle{\sin{{\left({t}+\pi\right)}}}={\sin{{t}}}{\cos{\pi}}+{\cos{{t}}}{\sin{\pi}}=-{\sin{{t}}}-{0}=-{\sin{{t}}}\)

Therefore

\(\displaystyle{\sin{{\left({t}+\pi\right)}}}=-{\sin{{t}}}=-{\frac{{{4}}}{{{5}}}}\)

Results:

\(\displaystyle{\sin{{\left({t}+\pi\right)}}}=-{\frac{{{4}}}{{{5}}}}\)

\(\displaystyle{\sin{{t}}}={\frac{{{4}}}{{{5}}}}\)

We need to find a value of

\(\displaystyle{\sin{{\left({t}+\pi\right)}}}\)

Remember that

\(\displaystyle{\sin{{\left({t}+\pi\right)}}}={\sin{{t}}}{\cos{\pi}}+{\cos{{t}}}{\sin{\pi}}=-{\sin{{t}}}-{0}=-{\sin{{t}}}\)

Therefore

\(\displaystyle{\sin{{\left({t}+\pi\right)}}}=-{\sin{{t}}}=-{\frac{{{4}}}{{{5}}}}\)

Results:

\(\displaystyle{\sin{{\left({t}+\pi\right)}}}=-{\frac{{{4}}}{{{5}}}}\)