Question

Calculati ctg a,stiind ca sin a =1 supra 3 si a∈(0 si pi supra 2).

Answer 1

$\it ctg a =\dfrac{cos a}{sin a} =\dfrac{\sqrt{1-sin^2 a}}{sin a}=\dfrac{\sqrt{1-\dfrac{1}{9}}}{\dfrac{1}{3}}=\dfrac{\sqrt{\dfrac{8}{9}}}{\dfrac{1}{3}} =\dfrac{\dfrac{2\sqrt2}{3}}{\dfrac{1}{3}} =2\sqrt2$

Answer 2

sqrt= radical, sqr= la patrat:
ctg a= (cos a)/(sin a), cos a=sqrt(1-sqr(sin(a)), cos a= sqrt(1-1/9)= 2*sqrt(2)/3=>
ctg a= (2*sqrt(2)/3)/(1/3)= 2*sqrt(2).