Question 1086583
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You have an angle {{{alpha}}} such that {{{sin(alpha)}}} = {{{2/5}}}.


In addition, you know that {{{alpha}}} is in QI.


Hence, cos{{{alpha)}}} = {{{sqrt(1-sin^2(alpha))}}} = {{{sqrt(1-(2/5)^2)}}} = {{{sqrt((25-4)/25)}}} = {{{sqrt(21)/5}}}.


Then {{{tan(alpha)}}} = {{{sin(alpha)/cos(alpha)}}} = {{{((2/5))/((sqrt(21)/5))}}} = {{{2/sqrt(21)}}} = {{{(2*sqrt(21))/21}}}.
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Solved.