# Thread: Just solving inverse trigometric function

1. ## Just solving inverse trigometric function

arctan(tan(11pi/5))

The textbook I have doesn't cover inverse trigonometric functions, at least for just solving them. I thought you would use (2pi - 11pi/5) but I get - pi/5 which is 36 degrees, as far as I know there isn't an angle on the unit circle that is 36 degrees.

2. $\displaystyle \arctan(\tan\left(\frac{11\pi}{5}\right)= \frac{11\pi}{5}$

as $\displaystyle \arctan$ and $\displaystyle \tan$ are inverse operations.

3. the answer here says its pi/5?

4. ok, what is the domain of $\displaystyle \arctan$ ?

5. [-infinity, infinity]

6. bump

7. The whole point of this problem is that for x between $\displaystyle -\pi/2$ and $\displaystyle \pi/2$, the domian of "principle value" of tangent, arctan(tan(x))= x. What angle between $\displaystyle -\pi/2$ and $\displaystyle \pi/2$ gives the same tangent as $\displaystyle 11\pi/5$?

(11/5= 2+ 1/5 so $\displaystyle 11\pi/5= 2\pi+ \pi/5$.)

### inverse trigomotric function.com

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