Question 820437: In each case, find sin(a), cos(a), csc(a), sec(a), and cot(a). Note: 'a' means alpha.
45. cos(2a)=3/5 and 0°<2a<90°
I've been trying to figure out this problem for some time, but I need help.
Found 2 solutions by stanbon, lwsshak3:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In each case, find sin(a), cos(a), csc(a), sec(a), and cot(a). Note: 'a' means alpha.
45. cos(2a)=3/5 and 0°<2a<90°
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cos = x/r
If cos(2a) = 3/5, x = 3 and r = 5
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Then y = sqrt[5^2-3^2] = sqrt[16] = 4
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And sin(2a) = y/r = 4/5
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Now use the half-angle formulas to get:
sin(2a/2) = sqrt[(1-cos(2a)/2] = sqrt[(1-(3/5))/2] = sqrt[1/5] = (1/5)sqrt(5)
cos(2a/2) = sqrt[(1+cos(2a)/2] = sqrt[(1+(3/5))/2] = sqrt(4/5) = (2/5)sqrt(5)
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tan(2a/2) = sin(2a/2)/cos(2a/2) = 1/2
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Note: csc(a), sec(a), cot(a) are the inverse of above.
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Cheers,
Stan H.
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Answer by lwsshak3(11628) (Show Source):
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