Abstract—In this paper, a fast and reliable formula for simplifying Sin⁴nθ and Cos⁴nθ using Half Angle Identities will be developed. This formula offers a simplified approach in simplifying sine and cosine function with exponent 4 to a function of cosine with exponent 1 with any value of n. From the algorithm of solving of half angle identities the new formula will emerge.

Index Terms—Mathematical algorithm, half angle identity, multiple angle formula, half angle formula, trigonometric identities.

F. G. Dampil is with the Malayan Colleges Laguna, Philippines (e-mail: fgdampil@mcl.edu.ph, fe_dampil@yahoo.com).

Cite: Fe G. Dampil, "Development of Trigonometric Formula for Sin⁴nθ and Cos⁴nθ Using Half Angle Identities as Mathematical Algorithm," International Journal of Applied Physics and Mathematics vol. 4, no. 3, pp. 155-158, 2014.