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

Jan 30, 2017

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

#### Explanation:

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

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 $x \in \left(- \infty , \infty\right)$.

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

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

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

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