Question

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

Answer 1

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

Explanation:

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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