SOLUTION: Find sin x/2, cos x/2, and tan x/2 from the given information. tan x = -4/3, x in quadrent 2

Question 1055520: Find sin x/2, cos x/2, and tan x/2 from the given information.
tan x = -4/3, x in quadrent 2

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find sin x/2, cos x/2, and tan x/2 from the given information.
tan x = -4/3, x in quadrant 2
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Since tan = y/x, y = 4 and x = -3
Then r = sqrt(4^2+3^2) = 5
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So, cos(x) = x/r = -3/5
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sin(x/2) = sqrt[(1-cos(x))/2] = sqrt[(1+(3/5))/2] = sqrt[4/5] = 2/sqrt(5)
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cos(x/2) = sqrt[(1-cos(x))/2] = sqrt[(1-(3/5))/2] = sqrt[1/5] = 1/sqrt(5)
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tan(x/2) = sin(x/2)/cos(x/2) = 2
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Cheers,
Stan H.
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