What is the value of \cos\frac{\pi}{4}

William Collins 2021-12-23 Answered
What is the value of \(\displaystyle{\cos{{\frac{{\pi}}{{{4}}}}}}\)

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intacte87
Answered 2021-12-24 Author has 4908 answers
Use the Unit Circle
\(\displaystyle{\cos{{\frac{{\pi}}{{{4}}}}}}={\left({\frac{{{1}}}{{\sqrt{{{2}}}}}}\right)}={\frac{{\sqrt{{{2}}}}}{{{2}}}}\)
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Jack Maxson
Answered 2021-12-25 Author has 2455 answers
It is possible to find the exact value of \(\displaystyle{\cos{{\frac{{\pi}}{{{4}}}}}}\) by constructing a right triangle with one angle set to \(\displaystyle{\frac{{\pi}}{{{4}}}}\) radians.
\(\displaystyle{\frac{{\pi}}{{{4}}}}{r}{a}{d}={\frac{{\pi}}{{{4}}}}{r}{a}{d}\times{\frac{{{180}°}}{{\pi}}}\times{r}{a}{d}^{{-{1}}}={45}°\)
Now draw a right triangle with one of the acute angles set to 45 degrees. These two angles would be supplementary, and their sum would be 90 degrees. Thus, the other angle in this triangle would also be 45 degrees, making an isosceles right triangle.
Therefore, \(\displaystyle{\cos{{\frac{{\pi}}{{{4}}}}}}={\cos{{\left({45}\right)}}}={\frac{{{a}{d}{j}.}}{{{h}{y}{p}.}}}={\frac{{{1}}}{{\sqrt{{{2}}}}}}={\frac{{\sqrt{{{2}}}}}{{{2}}}}\)
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user_27qwe
Answered 2021-12-30 Author has 9558 answers
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