Cognitive trust, the belief that a robot can accurately perform tasks, is crucial for effective human-robot interaction. While robot competence and reliability are known to build this trust, recent research shows that affective factors like attentiveness also matter. This study examines how competence and attentiveness interact to shape cognitive trust, specifically testing whether one factor can compensate for the other. Participants completed a search task with a robotic dog in a 2 × 2 design varying competence (high/low) and attentiveness (high/low). Results showed that high attentiveness compensates for low competence: participants working with an attentive but poorly performing robot reported trust levels similar to those working with highly competent robot. These findings suggest that building cognitive trust involves emotional processes often overlooked in traditional competence-based models.