\begin{aligned} \mathbf{f} \cdot \mathbf{f}^{\prime} &=[(\cos t) \mathbf{i}+(\sin t) \mathbf{j}] \cdot[-(\sin t) \mathbf{i}+(\cos t) \mathbf{j}] \\ &=-\cos t \sin t+\sin t \cos t=0 \end{aligned}