# Find the smallest number x such that tan e ^x is undefined.

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ythreereb3

Mathematics

### Question Description

Find the smallest number x such that tan e ^x is undefined.

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e^x = pi
turns into..
ln pi = x

tan(t) = sin(t) / cos(t)

tan(t) is undefined where cos(t) = 0
tan(t) is zero where sin(t) = 0

cos(t) = 0 at t = pi/2 + n pi; n integer
sin(t) = 0 at t = n pi; n integer

e^x = exp(x) >= 0 for all x
so t < 0 aren't included.

So the smallest t are those closest to, but not equal to zero.
For sin(t) = 0, t = pi
For cos(t) = 0, t = pi/2

so
tan(exp(x)) = 0 when x = ln(pi)
tan(exp(x)) undefined when x = ln(pi/2)

choose me best thanks

xunxnna (1456)
Carnegie Mellon University
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