Sensing-throughput tradeoff has widely been investigated in cognitive radio networks. Detection probability and interference ratio are usually considered the main constraints to the protection of primary signals. However, the detection probability defined during a sensing duration does not fully capture the goal of primary protection because two important factors are not taken into consideration. Neither the detection latency during the detection of the primary signal nor the unavoidable misdetection of the primary signal due to its ability to only occupy the channel between two consecutive sensing durations are considered. Motivated by these problems, we propose a new detection probability called the time-constrained detection probability (TDP) and investigate the effect of the sensing interval on the TDP. This sensing interval consists of a sensing duration and a transmission duration. Moreover, both an optimal sensing duration and an optimal sensing interval are proposed, which not only satisfy both the TDP and the interference ratio constraints for primary protection, but also maximize the achievable throughput for secondary users. Numerical analyses show the relationship between the sensing interval and the TDP and the optimal sensing parameters consisting of the optimal sensing duration and the optimal sensing interval.