Final answer:
The given equations represent the current (i) and voltage (v) as functions of time (t). The element in this case is a resistor.
Step-by-step explanation:
The given equations represent the current (i) and voltage (v) as functions of time (t). To find the element, we need to identify the relationship between the current and voltage. In this case, since i = cos(4t) and v = sin(4t), the element can be identified as a resistor. A resistor is an electrical component that follows Ohm's law, where the voltage across the resistor is directly proportional to the current passing through it. Therefore, the element in this case is a resistor.