Explain how to find the value of \cos(-45^{\circ}) using even-odd properties.

FizeauV 2021-08-17 Answered
Explain how to find the value of \(\displaystyle{\cos{{\left(-{45}^{{\circ}}\right)}}}\) using even-odd properties.

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Expert Answer

Malena
Answered 2021-08-18 Author has 18026 answers
Step 1
We know the even property that
\(\displaystyle{f{{\left(-{x}\right)}}}={f{{\left({x}\right)}}}\)
And we know that cos is an even function so, 1) \(\displaystyle{\cos{{\left(-{45}^{{\circ}}\right)}}}={\cos{{\left({45}^{{\circ}}\right)}}}\)
Step 2
We know the value of \(\displaystyle{\cos{{\left({45}^{{\circ}}\right)}}}={\frac{{{1}}}{{\sqrt{{{2}}}}}}.\)
Hence the value of \(\displaystyle{\cos{{\left(-{45}^{{\circ}}\right)}}}={\frac{{{1}}}{{\sqrt{{{2}}}}}}\) from equation(1).
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