Question 517822: what are the remaining five trigonometric func
tions of theta when sec theta = square root of 10, when tan > 0?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! what are the remaining five trigonometric functions
of theta when sec theta = square root of 10, when tan > 0?
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If sec theta > 0, theta is in Quadrant I or IV
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If tan theta > 0, theta is in the Quadrant I or III
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So theta is in QI where x,y, and r are all positive.
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So, sec(theta) = r/x means r = sqrt(10) and x = 1
Then y = sqrt[r^2-x^2]
y = sqrt[10-1] = 3
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sin = y/r = 3/sqrt(10)
cos = x/r = 1/sqrt(10)
tan = y/x = 3/1 = 3
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csc = r/y = sqrt(10)/3
sec = r/x = sqrt(10)
cot = x/y = 1/3
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Cheers,
Stan H.
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