Here's a question I'm having some trouble with:

given |x| = π / 4

What's the minimum value of: f(x) = (1 / (sec^2 x)) + sin x ?

I used desmos to graph both of these and this is what I got: https://ibb.co/QY9bDJs (is this type of image link acceptable?)

Would the leftmost point within the red highlighted part be the minimum value?

How can I get the minimum value without using graphing, and instead by using identities and such?

Thanks so much in advance!