Construction of two New Second Order Rotatable Designs Using Trigonometric Functions

In this study, two new second order rotatable designs of thirty-five and forty-five points are constructed respectively using transformations of some trigonometric functions. The designs are s rotatable since they satisfy both the outlined moment conditions and the non-singularity conditions. Second-order rotatable designs are useful for optimizing these processes in chemical industries, agriculture and engineering by systematically varying the factors of interest and studying their combined effects on the response variables. This helps in identifying the optimal settings for maximum or minimum responses.