Sine is negative in the 3rd and 4th quadrants.
Also note that if f(x) is a function and f^{-1}(x) is its inverse, then f^{-1}(f(a))=a
Find the exact value of the following. Draw a picture to help explain your answer.
sin^(-1)(sin(4π/3))
This is what I did:
sin^(-1)(sin(4π/3)) = sin^(-1)(-√3/2) = -π/3
Is this correct? I'm still not clear on how to determine which quadrant it should be in, but I guessed it would be quadrant 4 because the sine is negative.
Hi, thanks for your help. I understand that sine is negative in the 3rd and 4th quadrants. My question is what quadrant would π/3 be in? Or in other words, would a be positive or negative if f^-1(f(-a))?
Thanks again.
Do you not know what a "quadrant" is? A quadrant is 1/4 of a the plane or 1/4 of a circle so the "first quadrant" is from 0 to , the "second quadrant" is from to , the "third quadrant" is from to and the "fourth quadrant" is from to .
Thank you. I know what a quadrant is. I'm not a math major, but I have the courage to come here and ask about things I'm ignorant about because the people here are more knowledgeable about it than I am. I come here and very respectfully ask for help. I am here to learn, after all. I would appreciate being treated with respect as well.
You need to remember that the function is DEFINED so that you get an answer in the region . So even though your original angle was , you are correct that you will get an answer of , due to the original restriction made so that the function is one-to-one.
I can completely understand your frustration and even your thinking disrespect was given.
I can assure you that no disrespect was meant. We assume that you have certain basic knowledge.
In this case, the function has a domain of .
But more importantly, the range is
If you know those two facts then this whole thread is mute. In other words, knowing the basics answers most questions.