How do you evaluate $cos A = 0.5878$ $cos A = 0.5878$ ?

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Answer 1 · 2016-10-02T22:29:58

If by $0.5878$ $0.5878$ you mean

$\sqrt{\frac{5 - \sqrt{5}}{8}} = 0.5877852523$ $\sqrt{{5-\sqrt{5}}/8}=0.5877852523$

(to ten decimal places), then the answer is $A = \frac{3 π}{10}$ $A={3\pi}/{10}$ radians or $54°$ .

$cos(\pi/5)={\sqrt{5}+1}/4$ .

Then

$sin({3\pi}/{10})={\sqrt{5}+1}/4$

because ${3\pi}/{10}+\pi/5=\pi/2$ .

Then

$cos^2({3\pi}/{10})=1-sin^2({3\pi}/{10})=1-({\sqrt{5}+1}/4)^2={5-\sqrt{5}}/8$ .

How do you evaluate cos A = 0.5878cosA=0.5878cos A = 0.5878?