Phase angle

Symbol $\phi$. The AP Physics C: Mechanics table of information names it in the symbol list, plainly, as phase angle, and prints the equation it lives in:

EK 7.3.A.3 gives the same relation with $A$ for the amplitude and says that characteristics of SHM, such as velocity and acceleration, can be determined by or derived from it.

What it does. Setting $t = 0$ gives $x(0) = A\cos\phi$, so $\phi$ picks the starting point. It also picks the direction, since the velocity at $t=0$ carries a factor of $-\sin\phi$. Two useful anchors: $\phi = 0$ means released from rest at maximum displacement, and $\phi = -\pi/2$ turns the cosine into $A\sin(\omega t)$, which starts at the equilibrium position moving in the positive direction.

It is a time shift in disguise. A positive $\phi$ slides the whole curve earlier by $\phi/\omega$ seconds. Adding $2\pi$ to it changes nothing at all.

Radians, and not a physical angle. $\phi$ shares a unit with an angle because it is the argument of a cosine, but a block sliding on a spring is not rotating through anything. Reporting it in degrees inside an expression whose $\omega t$ term is in radians mixes two units in one bracket.

The algebra-based courses avoid it. AP Physics 1 EK 7.3.A.1 writes SHM as $x = A\cos(2\pi f t)$ or $x = A\sin(2\pi f t)$, and the AP Physics 2 sheet prints $x(t) = A\cos(\omega t)$. Choosing between sine and cosine is how those courses handle what $\phi$ handles in one equation.

See angular frequency for the $\omega$ it sits beside.