# Use the value of the trigonometric function to evaluate the indicated functions.

Use the value of the trigonometric function to evaluate the indicated functions. $$\displaystyle{\sin{{t}}}=\frac{{4}}{{5}},{\sin{{\left({t}+\pi\right)}}}$$

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