Hi,
I hope someone can help. Can someone please explain to me why sec^1(x) does NOT equal 1/cos^1(x) and why sec^1(x) does equal cos^1(1/x)?
The notation can get a bit confusing.
Thanks,
Olivia
Do you know how to find the inverse of a function $f(x)$?
Write $$f(x) = \frac{1}{\cos(x)}=y$$
Interchange the $x$ and $y$ to get
$$\frac{1}{\cos(y)}=x$$
Isolate $y$,
$$\cos(y)= \frac{1}{x}$$
$$y= \cos^{-1} \left(\frac{1}{x}\right)$$
Which is $f^{-1}(x)$.