sin² = 1/2 (1 - cos 2)
cos² = 1/2 (1 + cos 2)

sin³ = 1/4 (3sin - sin 3)
cos³ = 1/4 (3cos + cos 3)

sin⁴ = 1/8 (cos 4 - 4cos 2 + 3)
cos⁴ = 1/8 (cos 4 + 4cos 2 + 3)

sin⁵ = 1/16 (10sin - 5sin 3 + sin 5)
cos⁵ = 1/16 (10cos + 5cos 3 + cos 5)

sin⁶ = 1/32 (10 - 15cos 2 + 6cos 4 - cos 6)
cos⁶ = 1/32 (10 + 15cos 2 + 6cos 4 + cos 6)