The rotation `ry(θ)` turns a qubit's state through an angle θ/2 between |0⟩ and |1⟩:

ry(θ)|0⟩ = cos(θ/2)|0⟩ + sin(θ/2)|1⟩,

so the probability of 1 is sin²(θ/2). θ = π gives a certain 1, as `x` does; θ = π/2 gives one half, as `h` does.

Angles change how the engine computes. An angle that is a multiple of 2π/2ᵏ (π, π/2, π/4, …) runs on the *bit-exact* method, the same bits on every machine. Any other angle runs in double precision, accurate to rounding, and the result says so in its accuracy class. The check of a distribution is exact either way, within a tolerance of 10⁻⁹ for rounding.

```sh runnable
cat > turn.qasm <<'QASM'
OPENQASM 3.0;
include "stdgates.inc";
qubit[1] q;
rx(0.3) q[0];
QASM
wai-quantum plan turn.qasm
```