Question 921352
Suppose sec t = 2 and csc t > 0. Find each of the following:
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Note: Since sec and csc are both positive, t is in QI where x and y are pos.
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cos t = 1/sec(t) = 1/2
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cos (−t) =  1/2 because cos(t) = cos(-t)
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cos (π + t) = -1/2 because adding pi to the angle throws it into QIII
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sin (−t) = 
Since sec = 2 = r/y, x = sqrt[2^2-1^2] = sqrt(3)
So, sin(t) = sqrt(3)/2
Therefore sin(t) = -sqrt(3)/2 because the negative puts the angle into QIV
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tan (t + π) = 
tan = sin/cos = (sqrt(3)/2)(1/2) = sqrt(3)
So, tan(t+pi) = sqrt(3) since adding pi puts the angle in QIII where sin
and cos are both negative.
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Cheers,
Stan H.
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