A root of a "saw-like" function

Question

Say, we have f(t) = v * t + A * sin(w * t). I call such functions "saw-like":

I want to solve saw(t) = C, that is, find a root of saw(t) - C (still "saw-like").

I tried writing down a ternary search for function abs(saw(t) - C) to find its minima. If we are lucky (or crafty), it would be the root. Unfortunately, my code does not always work: sometimes we get stuck in those places:

My code (python3):

def calculate(fun):
    eps = 0.000000001
    eps_l = 0.1
    x = terns(fun, 0, 100000000000000)
    t = terns(fun, 0, x)
    cnt = 0
    while fun(x) > eps:
        t = x
        x = terns(fun, 0, t)
        if abs(t - x) < eps_l:
            cnt += 1
        # A sorry attempt  pass some wrong value as a right one. 
        # Gets us out of an infinite loop at least.
        if cnt == 10:
            break
    return t

def terns(f, l, r):
    eps = 0.00000000001
    while r - l > eps:
        x_1 = l + (r - l) / 3
        x_2 = r - (r - l) / 3

        if f(x_1) < f(x_2):
            r = x_2 
        else:
            l = x_1
    return (l + r) / 2

So, how is it done? Is using ternary search the right way?

---

My other idea was somehow sending the equation over to the net, passing it to Wolfram Alpha and fetching the answers. Yet, I don't how it's done, as I am not quite fluent at python.

How could this be done?