Final answer:
The general solutions for the equation sin⁴(x) = 0 are found at angles where the sine function equals zero, which is at x = nπ, where n is an integer.
Step-by-step explanation:
The equation sin⁴(x) = 0 can be solved by using trigonometric identities. Since sin⁴(x) is just (sin(x))^4, we are looking for angles where the sine is zero. The sine of an angle is zero when the angle is a multiple of π, or nπ where n is an integer. Hence, the general solution for x in sin⁴(x) = 0 is x = nπ, where n is an integer.