Question 889028: Find the exact values of sin(θ/2), cos(θ/2), and tan(θ/2) for the given conditions. sec θ = −3/2; 180° < θ < 270° I need help!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the exact values of sin(θ/2), cos(θ/2), and tan(θ/2) for the given conditions. sec θ = −3/2; 180° < θ < 270°
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By definition, sec(t) = r/x
So r = 3 and x = -2
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Then y = -sqrt(3^2+2^2) = -sqrt(13) in QIII
And cos(t) = -2/3 in QIII
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Answers:
sin(t/2) = sqrt[(1-cos(t))/2] = sqrt[(1+(2/3))/2 = sqrt(5/6)
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cos(t/2) = sqrt[(1+cos(t))/2[ = sqrt[(1-(2/3))/2] = sqrt(1/6)
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tan(t/2) = sin(t/2)/cos(t/2) = sqrt(5/6)/sqrt(1/6) = sqrt(5)
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Cheers,
Stan H.
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