# Thread: Which of the following is not defined?

1. ## Which of the following is not defined?

Arcsin(1/9)
Arccos(-4/3)
Arctan(11/12)
Arccot(-4)
Arcsec(3Pi)

What exactly is to define a function?
NOw the answer to this is supposed to be Arccos(-4/3) because $-1\leq cos(x) \leq+1$

Is Cos(x) between -1 and +1 because it is DEFINED that way?

What about arcsec(3Pi)? Is that defined? Isn't arcsec 3Pi = 1/(arccos 3Pi)? and again isn't 3Pi greater than 1 thereby rendering it undefined because $-1\leq cos(x) \leq+1$

?????

2. Originally Posted by Utterconfusion
Arcsin(1/9)
Arccos(-4/3)
Arctan(11/12)
Arccot(-4)
Arcsec(3Pi)

What exactly is to define a function?
NOw the answer to this is supposed to be Arccos(-4/3) because $-1\leq cos(x) \leq+1$

Is Cos(x) between -1 and +1 because it is DEFINED that way?

What about arcsec(3Pi)? Is that defined? Isn't arcsec 3Pi = 1/(arccos 3Pi)? and again isn't 3Pi greater than 1 thereby rendering it undefined because $-1\leq cos(x) \leq+1$

?????
You are confusing the reciprocal function with the inverse function:

$sec(x)=\frac{1}{cos(x)}$ and $\theta = arccos(x)$

Actually, if you work it out you will find that $arcsec(x) = arccos(\frac{1}{x})$ and not $\frac{1}{arccos(x)}$

This means that $arcsec(3\pi) = arccos(\frac{1}{3\pi})$

arcsec is defined everywhere EXCEPT between -1 and 1.