SOLUTION: please help me how would i solve: Use the fact that tan(beta)=4 to find: cot(beta),cos(beta)sec(beta) and csc(beta)

Question 619103: please help me
how would i solve:
Use the fact that tan(beta)=4 to find:
cot(beta),cos(beta)sec(beta) and csc(beta)
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
solve:
Use the fact that tan(beta)=4 to find:
cot(beta),cos(beta)sec(beta) and csc(beta)
----
You didn't say what Quadrant beta was in; I'll assume
it is in the 1st Quadrant where everything is positive.
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tan = y/x
Since y/x = 4, y = 4 and x = 1
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Then r = sqrt(x^2+y^2) = sqrt(17)
----
So,
cot = x/y = 1/4
cos = x/r = 1/sqrt(17)
sec = r/x = sqrt(17)
csc = r/y = sqrt(17)/4
==============================
cheers,
Stan H.

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
tan is the ratio of the two legs

if the legs are 4 and 1; then (by Pythagoras) the hypotenuse is √17

cot = 1 / tan

cos = 1 / √17

sec = 1 / cos

csc = √17 / 4
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