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

Cabiolab 2021-10-16 Answered
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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Expert Answer

Aubree Mcintyre
Answered 2021-10-17 Author has 8283 answers
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:
\(\displaystyle{\sin{{\left({t}+\pi\right)}}}=-{\frac{{{4}}}{{{5}}}}\)
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