Question 760624
cosecant theta = 9
and
Cotangent theta = 3
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Draw a right triangle and use the pythagoeran theorem to determine the third side and find the five remaining logarithmic functions of theta.
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csc = r/y = 9/1
So r = 9 and y = 1
Solve for "x":
x = sqrt[r^2-y^2] = sqrt[81-1] = sqrt(80) = 4sqrt(5)
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sin = y/r = 1/9
cos = x/r = (4/9)sqrt(5)
tan = y/x = 1/(4sqrt(5))
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csc = r/y = 9
sec = r/x = 9/(4sqrt(5))
cot = x/y = 4sqrt(5)
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cot = x/y = 3/1
So x = 3 and y = 1
r = sqrt(x^2 + y^2) = sqrt(9+1) = sqrt(10)
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sin = y/r = 1/sqrt(10)
cos = x/r = 3/sqrt(10)
tan = y/x = 1/3
csc = r/y = sqrt(10)
sec = r/x = sqrt(10)/3
cot = x/y = 3/1 = 3
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Cheers,
Stan H.
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