# Find exact value of \cos (\frac{9\pi}{4}) How do you get (\frac

facas9 2021-08-13 Answered
Find exact value of $$\displaystyle{\cos{{\left({\frac{{{9}\pi}}{{{4}}}}\right)}}}$$
How do you get $$\displaystyle{\left({\frac{{\pi}}{{{4}}}}+{2}\pi\right)}$$

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## Expert Answer

wheezym
Answered 2021-08-14 Author has 13806 answers
$$\displaystyle{\frac{{{9}\pi}}{{{4}}}}={\frac{{\pi}}{{{4}}}}+{\frac{{{8}\pi}}{{{4}}}}={\frac{{\pi}}{{{4}}}}+{2}\pi$$
so $$\displaystyle{\frac{{\pi}}{{{4}}}}$$ is the reference angle $$\displaystyle\angle{45}^{{{o}}}$$
$$\displaystyle{\cos{{\left({\frac{{\pi}}{{{4}}}}\right)}}}={\frac{{\sqrt{{{2}}}}}{{{2}}}}$$

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