Can you have a cosine graph that starts at 0, but the 3rd key point is above 0?

Answer 1

If you shift cosine a little bit to the right (90 degrees or π/2) - it will become exactly as sin - starting from 0, rising to 1, dropping to -1 and back to 0.

If you need it to drop first instead of rising, you just invert it (having a coefficient -1 in-front).

So with the mentioned shift, your function will be

cos ( x - π/2) for the "rising first function or

-cos ( x - π/2) for the one dropping down first