SOLUTION: cosecant theta 9 and Cotangent theta 3 Draw a right triangle and use the pythagoeran theorem to determine the third side and find the five remaining logarithmic functions of the

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Question 760624: cosecant theta 9
and
Cotangent theta 3
Draw a right triangle and use the pythagoeran theorem to determine the third side and find the five remaining logarithmic functions of theta.
THANKYOU
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Logarithms have nothing whatever to do with right triangles. And what are you trying to say with "cosecant theta 9" Do you mean ?

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
cosecant theta = 9
and
Cotangent theta = 3
-----------------------------
Draw a right triangle and use the pythagoeran theorem to determine the third side and find the five remaining logarithmic functions of theta.
------
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)
-----
sin = y/r = 1/9
cos = x/r = (4/9)sqrt(5)
tan = y/x = 1/(4sqrt(5))
----
csc = r/y = 9
sec = r/x = 9/(4sqrt(5))
cot = x/y = 4sqrt(5)
============================
cot = x/y = 3/1
So x = 3 and y = 1
r = sqrt(x^2 + y^2) = sqrt(9+1) = sqrt(10)
-----------
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
=========================
Cheers,
Stan H.
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