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If 1-cos(angle) / sin(angle) = sqrt3 / 3,

 

what is angle? show proof

 Sep 12, 2020
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If 1-cos(angle) / sin(angle) = sqrt3 / 3,
what is angle? show proof

 

Hello Guest!

 

\(1-\frac{cos (x)}{sin (x)}=\frac{\sqrt{3}}{3}\)           \(1-\frac{cos (67.732deg)}{sin (67.732deg)}=\frac{\sqrt{3}}{3}\)

                                       \(1-0.42265=0.57735\)

 

\(\frac{1}{1-\frac{cos (x)}{sin (x)}}=\frac{3}{\sqrt{3}}\\ \frac{1}{1-cot(x) }=\sqrt{3}\\ 1=\sqrt{3}-cot(x)\cdot\sqrt{3}\\ cot(x)\cdot\sqrt{3}= \sqrt{3}-1\)

\(cot(x)=1-\frac{\sqrt{3}}{3}\)

 

\(angle\ (x) = 67.732\ deg\)

laugh  !

 Sep 12, 2020
edited by asinus  Sep 12, 2020

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