Question 387952
Let {{{alpha = cos^(-1)(-4/7)}}}.  Then {{{cos(alpha) = -4/7}}}, and we have to find the value of {{{tan(alpha)}}}.  Now {{{cos(alpha) = -4/7}}}---->{{{sec(alpha) = -7/4}}}, so that, by using the identity {{{(sec(alpha))^2 = 1 + (tan(alpha))^2}}}, we get {{{49/16 = 1 +  (tan(alpha))^2}}}, or {{{33/16 = (tan(alpha))^2}}}.
Then {{{tan(alpha) = -sqrt(33)/4}}}.  Tangent of {{{alpha}}} is negative because {{{cos^(-1)(-4/7)}}} means {{{alpha}}} is in the 2nd quadrant.