6. Given point $P(x, y)$ lies on the curve $C$:
$$
(x \cos \theta + y \sin \theta)^{2} + x \sin \theta - y \cos \theta = 1
$$

Then the minimum value of $|O P|$ (where $O$ is the origin) is ( ).
(A) $\frac{1}{2}$
(B) $\frac{\sqrt{2}}{2}$
(C) $\frac{\sqrt{3}}{2}$
(D) 1
6.C.

Let \( u = x \cos \theta + y \sin \theta, v = x \sin \theta - y \cos \theta \).
Then \( u^{2} + v = 1 \), and we have
\[
\begin{array}{l}
u^{2} + v^{2} = (x \cos \theta + y \sin \theta)^{2} + (x \sin \theta - y \cos \theta)^{2} \\
= x^{2} + y^{2} .
\end{array}
\]
\[
\begin{array}{l}
\text { Hence } |OP| = \sqrt{x^{2} + y^{2}} = \sqrt{u^{2} + v^{2}} = \sqrt{v^{2} - v + 1} \\
= \sqrt{\left(v - \frac{1}{2}\right)^{2} + \frac{3}{4}} \geqslant \frac{\sqrt{3}}{2} .
\end{array}
\]