Question 863561: Find the exact value of:
sin(2cos^-1(24/25))
and
tan(cos^-1(1/5))
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the exact value of:
sin(2cos^-1(24/25))
Note: sin(2t) = 2sin(t)*cos(t)
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Since cos = (24/25), sin = sqrt(25^2-24^2)/25 = 7/25
Therefore: sin(2cos^-1(24/25)) = 2(7/25)(24/25) = 0.5376
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and
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tan(cos^-1(1/5))
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Let t = cos-1(1/5)
Since cos(t) = 1/5, x = 1 and r = 5
Then y = sqrt(5^2-1^2) = 2sqrt(6)
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Ans: tan(t) = y/x = (2sqrt(6))/1 = 2sqrt(6)
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Cheers,
Stan H.
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