Before this question is removed for being a duplicate, let me specify what I'm looking for.
The book should have a treatment of the foundations of periodic/trigonometric functions. Students are often stumped at what these periodic functions really are. In a simple quadratic formula, you just square every input value and create an output by doing so. In trig/periodic functions, this isn't quite as clear.
The book should touch on more advanced trig/periodic topics, if even just slightly.
The book should have an in-depth discussion on the anatomy of sine and cosine functions. Too often do books keep their discussion of "c" in $a+b\sin(c(x-d))$ limited to "c is two pi divided by the period", not giving students a feel or intuition for the way it impacts your function and what it represents.
Students are acquainted with basic proof-writing.
I should also specify that Fourier series or advanced calculus can't be in the book. It has to be accessible to freshmen.
Something like Gelfand's "Trigonometry", only slightly more advanced and fundamental. Mostly geared towards a fundamental audience.