The question asks for the exact value of the trignometric function at the given

Chaya Galloway 2021-08-20 Answered
The question asks for the exact value of the trignometric function at the given real number:
\(\displaystyle{\sin{{\left({\frac{{{7}\pi}}{{{4}}}}\right)}}}\) I answered \(\displaystyle{\left({\frac{{-\sqrt{{{2}}}}}{{{2}}}}\right)}\)

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Expert Answer

avortarF
Answered 2021-08-21 Author has 10490 answers
To find the exact value of \(\displaystyle{\sin{{\left({\frac{{{7}\pi}}{{{4}}}}\right)}}}\)
Using trigonometry table and trigonometry unit circle
\(\displaystyle{\sin{{\left({\frac{{{7}\pi}}{{{4}}}}\right)}}}={\sin{{\left(-{\frac{{\pi}}{{{4}}}}+{\frac{{{8}\pi}}{{{4}}}}\right)}}}\)
\(\displaystyle={\sin{{\left(-{\frac{{\pi}}{{{4}}}}+{2}\pi\right)}}}\)
\(\displaystyle={\sin{{\left(-{\frac{{\pi}}{{{4}}}}\right)}}}\)
\(\displaystyle=-{\sin{{\left({\frac{{\pi}}{{{4}}}}\right)}}}\)
\(\displaystyle=-{\frac{{\sqrt{{{2}}}}}{{{2}}}}\)
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