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

2020-10-27
The fromula:
$$\displaystyle{\cos{{\left({x}\right)}}}={\sin{{\left({90}^{\circ}-{x}\right)}}}$$
Substitute the given angle:
$$\displaystyle{\cos{{\left({72}^{\circ}\right)}}}={\sin{{\left({90}^{\circ}-{72}^{\circ}\right)}}}$$
$$\displaystyle{\cos{{\left({72}^{\circ}\right)}}}={\sin{{\left({18}^{\circ}\right)}}}$$
$$\displaystyle=\frac{{\sqrt{{2}}\sqrt{{{3}-\sqrt{{5}}}}}}{{4}}$$
$$\displaystyle\approx{0.30901}$$

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