Suppose cos(x) = u, how do you write tan(x) in terms of x?

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Answer 1 · 2016-07-16T09:27:37

# tan(x) = (sin(x))/(cos(x))#

Remember from SOH CAH TOA that

#costheta = ("Adjacent")/("Hypotenuse")#

We can use this to construct a triangle.

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From the triangle, we see that

#tan(x) = (sqrt(1-u^2))/u#

#tan(x) = (sqrt(1-cos^2(x)))/(cos(x)) = (sqrt(sin^2(x)))/cos(x) #

#therefore tan(x) = (sin(x))/(cos(x))#