Pre-Calculus/Trigonometry Problem:

Question

anonymous · Answer

Does $$\tan^{-1} (\tan \frac{ 2\pi }{ 3 })=\frac{ 2\pi }{ 3 }$$ Why or why not?

anonymous · Answer

@ganeshie8

anonymous · Answer

it's like $$f ^{-1} (f (x)) = x$$

anonymous · Answer

how would you explain that using 2pi/3

anonymous · Answer

my teacher wants us to explain it using that number

anonymous · Answer

it's the same idea. you just replace x with 2pi/3

anonymous · Answer

there must be some reasoning behind that

campbell_st · Answer

well the solution is partly correct... and tan is positive in 2 quadrants... so you need to look at the domain to see if there are any restictions before answering

campbell_st · Answer

oops 2pi/3 is negative.... but still 2 possible solutions withing the domain [0, 2pi]

anonymous · Answer

i don't know what to write as my answer... I'm kind of confused

anonymous · Answer

@Zale101 any ideas?

zale101 · Answer

Let's say we have, $sin(\theta)=0$
This equation interprets: The sine of what angle $\theta$ is equal to ½
A good answer for this would be:
"The angle whose sine is 0 is $\pi$"
Which in an equation form, it would be written as this for the answer:
$sin^{-1}(\pi)=0$


$tan^{-1}$ stands for tangent whose angle is $tan(\frac{2\pi}{3})$ and the angle of tangent is in radian which is 2pi/3