Question 1094706
.
tan(sin^-1(1/7))
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<pre>
{{{sin^(-1)(1/7)}}}  is  {{{arcsin(1/7)}}}.


So,  they want you calculate  {{{tan(alpha)}}},  where {{{alpha)}}} = {{{arcsin(1/7)}}}.


Since  {{{alpha)}}} = {{{arcsin(1/7)}}},  it means that  {{{sin(alpha)}}} = {{{1/7}}}.


Then  {{{cos(alpha)}}} = {{{sqrt(1-sin^2(alpha))}}} = {{{sqrt(1-(1/7)^2)}}} = {{{sqrt(1-1/49)}}} = {{{sqrt((49-1)/49)}}} = {{{sqrt(48)/7}}} = {{{(4*sqrt(3))/7}}}.


Finally,   {{{tan(alpha)}}} = {{{sin(alpha)/cos(alpha)}}} = {{{((1/7))/((4*sqrt(3))/7)}}} = {{{1/(4*sqrt(3))}}} = {{{sqrt(3)/12}}}.
</pre>


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