FizeauV

2020-10-26

What is the value $\mathrm{cos}\left({72}^{\circ }\right)$? Write your answer in decimals.

Demi-Leigh Barrera

The formula:
$\mathrm{cos}\left(x\right)=\mathrm{sin}\left({90}^{\circ }-x\right)$
Substitute the given angle:
$\mathrm{cos}\left({72}^{\circ }\right)=\mathrm{sin}\left({90}^{\circ }-{72}^{\circ }\right)$
$\mathrm{cos}\left({72}^{\circ }\right)=\mathrm{sin}\left({18}^{\circ }\right)$
$=\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}$
$\approx 0.30901$

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