How do you evaluate $arccos (\frac{1}{2 \cdot \sqrt{2}})$ $arccos(1/(2*sqrt(2)))$ ?

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How do you evaluate $arccos (\frac{1}{2 \cdot \sqrt{2}})$ $arccos(1/(2*sqrt(2)))$ ?

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Answer 1 · 2017-03-25T17:50:38

$a r c cos (\frac{1}{2 \sqrt{2}}) = {69.3}^{\circ}$ $arc cos(1/(2sqrt2))=69.3^@$

Explanation:

Let $a r c cos (\frac{1}{2 \sqrt{2}}) = A$ $arc cos(1/(2sqrt2))=A$

then $cos A = \frac{1}{2 \sqrt{2}} = \frac{\sqrt{2}}{4} = 0.35355$ $cosA=1/(2sqrt2)=sqrt2/4=0.35355$

and using tables or scientific calculator

$A = {69.3}^{\circ}$ $A=69.3^@$

Answer 2 · 2017-03-25T22:21:21

$x = \pm 69^{\circ} 30 + k 360^{2}$ $x = +- 69^@30 + k360^2$

Explanation:

$cos x = \frac{1}{2 \sqrt{2}} = \frac{\sqrt{2}}{4} = 0.3535$ $cos x = 1/(2sqrt2) = sqrt2/4 = 0.3535$
Calculator and unit circle give -->
$x = \pm 69^{\circ} 30 + k 360^{\circ}$ $x = +- 69^@30 + k360^@$

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