How do you find the domain and range of $tan(cos(x))$ ?

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Answer 1 · 2017-01-30T12:03:00

Domain : $x in (-oo, oo)$
Range : $[tan(-1)), tan(1)]=[-1.5574, 1.5574]$ , nearly.
Socratic graph is inserted.

As the range of cos x is $[-1, 1]$ ,

the range of #tan(cosx is [tan(-1), tan 1]= [-1.5574, 1.5574], nearly.

Noe that 1 in tan 1 is 1 radian = $57.3^o$ , nearly.

Of course, the function is defined for this range,

with $x in (-oo, oo)$ .

See the second graph for one period, $x in [-pi, pi]$ .

graph{arctany=cosx [-10, 10, -5, 5]}

graph{arctany-cosx=0 [-3.14, 3.14, -1.57, 1.57]}

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How do you find the domain and range of tan(cos(x))tan(cos(x))?