**Inputs:**

1. Angle $\alpha$, in radians, represented as Double.
2. A qubit in state $|\psi\rangle = \beta |0\rangle + \gamma |1\rangle$.

**Goal:** Change the state of the qubit as follows:

- If the qubit is in state $|0\rangle$, change its state to $\cos \alpha |0\rangle + \sin \alpha |1\rangle$.
- If the qubit is in state $|1\rangle$, change its state to $-\sin \alpha |0\rangle + \cos \alpha |1\rangle$.
- If the qubit is in superposition, change its state according to the effect on basis vectors.
