O otownsend Mar 2017 358 3 Massachusetts Jun 12, 2017 #1 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

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

Ahri Dec 2016 31 12 United Kingdom Jun 12, 2017 #2 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 $f^{-1}(x)$.

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 $f^{-1}(x)$.