Question 352071: 1) sec (theta)= -(25/24), theta lies in quadrant II, find sin (theta/2)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1) sec (theta)= -(25/24), theta lies in quadrant II,
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Fact: sec = r/x where x is negative in the QII.
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So, x = -24 and r = 25
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y = sqrt(r^2-x^2)
y = sqrt(49) = 7 which is positive in QII
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So, sin(theta) = 7/25 and cos(theta) = -24/25
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find sin (theta/2) = sqrt[(1-cos(theta))/2]
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= sqrt[(1-(-24/25))/2]
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= sqrt[(25+24)/50]
= sqrt[49/50]
= 7sqr(50)/50
= 35sqrt(2)/50
= (7/10)sqrt(2)
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Cheers,
Stan H.
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