Usually every simple harmonic question starts with the line: The block at equilibrium shifted to a position $X_0$ and released.
I found this from the website: https://study.com/academy/lesson/simple-harmonic-motion-shm-definition-formulas-examples.html
This equation has a sine in it, and a sine graph starts at zero. Using this equation is like starting your mathematical stopwatch in the middle of a pendulum swing: $t = 0$ is in the center of the oscillation. If, on the other hand, you replace sine with a cosine, then the equation is still correct; you're just starting to measure time at the maximum displacement instead.
Now if this holds true then most of my question in my textbook in which the mass is slightly displaced from an equilibrium point uses the $\sin$ equation instead of $\cos$. Aren't we measuring motion from the Amplitude point at $t=0$... Why the discrepancy?