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

Question

2754 views around the world

You can reuse this answer
Creative Commons License

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]}

.