anonymous
  • anonymous
find the exact value of tan x/2, givin that sin x=8/17 and 90degrees
Mathematics
chestercat
  • chestercat
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dumbcow
  • dumbcow
For this problem you need to use your trig half-angle formulas sin(x/2) = sqrt((1-cosx)/2) cos(x/2) = sqrt((1+cosx)/2) tanx = sinx/cosx so tan(x/2) = sin(x/2)/cos(x/2) ->tan(x/2) = sqrt((1-cosx)/2) / sqrt((1+cosx)/2) But now the function is defined in terms of cosx and we are given value of sinx so we use a trig identity sin^2 + cos^2 = 1 -> cosx = sqrt(1-sinx^2) -> cosx = sqrt(1-(8/17)^2) = sqrt((17^2-64)/17^2) = 15/17 sub that into the above equation for cosx with a little simplifying ->tan(x/2) = sqrt(1/17) / sqrt(16/17) = (1/sqrt(17))*(sqrt(17)/sqrt(16)) = 1/4
dumbcow
  • dumbcow
actually tan(x/2) = -1/4 due to restrictions on x remember 1/sqrt(16) = +-(1/4)

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