SOLUTION: how would I complete the steps? of if cos(t) = 1/4 and 0 < t < pi/2, then cos(pi/6+t) = ???

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Question 626547: how would I complete the steps? of if cos(t) = 1/4 and 0 < t < pi/2, then cos(pi/6+t) = ???
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
how would I complete the steps? of if cos(t) = 1/4 and 0 < t < pi/2, then cos(pi/6+t) = ???
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Note: if cos(t) = 1/4, then x = 1 and r = 4
Therefore y = sqrt(r^2-x^2) = sqrt(16-1) = sqrt(15)
So sin(t) = y/r = sqrt(15)/4
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cos((pi/6)+t) = cos(pi/6)*cos(t) - sin(pi/6)*sin(t)
cos((pi/6)+t) = [sqrt(3)/2]*(1/4) - (1/2)(sqrt(15)/4)
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= sqrt(3)/8 - sqrt(15)/8
= (sqrt(3)-sqrt(15))/8
is approximately -0.2676..
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Cheers,
Stan H.
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