+15001 If 1-cos(angle) / sin(angle) = sqrt3 / 3,
what is angle? show proof
Hello Guest!
\(1-\frac{cos (x)}{sin (x)}=\frac{\sqrt{3}}{3}\) \(1-\frac{cos (67.732deg)}{sin (67.732deg)}=\frac{\sqrt{3}}{3}\)
\(1-0.42265=0.57735\)
\(\frac{1}{1-\frac{cos (x)}{sin (x)}}=\frac{3}{\sqrt{3}}\\ \frac{1}{1-cot(x) }=\sqrt{3}\\ 1=\sqrt{3}-cot(x)\cdot\sqrt{3}\\ cot(x)\cdot\sqrt{3}= \sqrt{3}-1\)
\(cot(x)=1-\frac{\sqrt{3}}{3}\)
\(angle\ (x) = 67.732\ deg\)
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