This paper is dedicated to study the sine version of polar bodies and establish the Lp-sine Blaschke-Santaló inequality for the Lp-sine centroid body.The Lp-sine centroid body ΛpK for a star body K⊂Rn is a convex body based on the Lp-sine transform, and its associated Blaschke-Santaló inequality provides an upper bound for the volume of Λp∘K, the polar body of ΛpK, in terms of the volume of K. Thus, this inequality can be viewed as the “sine cousin” of the Lp Blaschke-Santaló inequality established by Lutwak and Zhang. As p→∞, the limit of Λp∘K becomes the sine polar body K⋄ and hence the Lp-sine Blaschke-Santaló inequality reduces to the sine Blaschke-Santaló inequality for the sine polar body. The sine polarity naturally leads to a new class of convex bodies Cen, which consists of all origin-symmetric convex bodies generated by the intersection of origin-symmetric closed solid cylinders. Many notions in Cen are developed, including the cylindrical support function, the supporting cylinder, the cylindrical Gauss image, and the cylindrical hull. Based on these newly introduced notions, the equality conditions of the sine Blaschke-Santaló inequality are settled.