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Find-the-value-of-cos-1-isin-1-cos-2-isin-2-cos-359-isin-359-

Question Number 137468 by ZiYangLee last updated on 03/Apr/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\left(\mathrm{cos}\:\mathrm{1}°+{i}\mathrm{sin}\:\mathrm{1}°\right)\left(\mathrm{cos}\:\mathrm{2}°+{i}\mathrm{sin}\:\mathrm{2}°\right)\ldots\left(\mathrm{cos}\:\mathrm{359}°+{i}\mathrm{sin}\:\mathrm{359}°\right). \\ $$ Answered by mr W last updated on 03/Apr/21 $$={e}^{\frac{\mathrm{1}}{\mathrm{180}}\pi{i}} {e}^{\frac{\mathrm{2}}{\mathrm{180}}\pi{i}} …{e}^{\frac{\mathrm{359}}{\mathrm{180}}\pi{i}}…

Question-137467

Question Number 137467 by SOMEDAVONG last updated on 03/Apr/21 Answered by Ñï= last updated on 03/Apr/21 $${I}=\int\frac{{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} }{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx}=\int\frac{{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} }{{i}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}=\frac{\mathrm{1}}{{i}}\int{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} {d}\left(\mathrm{sin}^{−\mathrm{1}}…

There-are-3-tangent-circumferences-inscribed-in-an-isosceles-right-triangle-Two-of-these-circumferences-have-radius-R-and-are-tangent-to-the-hypotenuse-and-to-the-two-cathetus-The-smaller-circumfere

Question Number 71819 by Maclaurin Stickker last updated on 20/Oct/19 $${There}\:{are}\:\mathrm{3}\:{tangent}\:{circumferences} \\ $$$${inscribed}\:{in}\:{an}\:{isosceles}\:{right}\:{triangle} \\ $$$${Two}\:{of}\:{these}\:{circumferences}\:{have} \\ $$$${radius}\:\boldsymbol{{R}}\:{and}\:{are}\:{tangent}\:{to}\:{the}\: \\ $$$${hypotenuse}\:{and}\:{to}\:{the}\:{two}\:{cathetus}. \\ $$$${The}\:{smaller}\:{circumference}\:{has}\: \\ $$$${radius}\:\boldsymbol{{r}}\:{and}\:{is}\:{tangent}\:{to}\:{the}\:{two} \\ $$$${cathetus}.\:{How}\:{can}\:{I}\:{find}\:{the}\:{radius}…