# Graphing Trig Functions

• October 16th 2011, 08:47 PM
Manni
Graphing Trig Functions
Is arctan(tan(2x)) an example of a composite function? In other words, would the range of tan2x become the domain of arctanx? Also, is the domain for this composite function the union between the domains of tan2x and arctanx?
• October 16th 2011, 10:32 PM
Prove It
Re: Graphing Trig Functions
Quote:

Originally Posted by Manni
Is arctan(tan(2x)) an example of a composite function? In other words, would the range of tan2x become the domain of arctanx? Also, is the domain for this composite function the union between the domains of tan2x and arctanx?

Since the tangent and arctangent functions are inverse functions, this is just 2x...
• October 17th 2011, 12:15 AM
Deveno
Re: Graphing Trig Functions
Quote:

Originally Posted by Prove It
Since the tangent and arctangent functions are inverse functions, this is just 2x...

not quite. what if $x = \frac{\pi}{4}$...?

also, the range of arctan is (-1,1). but we can easily imagine an original input of, oh say 2.

see for yourself: y &#61; arctan&#40;tan&#40;2x&#41;&#41; - Wolfram|Alpha

the function is not defined for all real x, and is not even equal to 2x except on (-pi/4,pi/4).