The Eighth Gate Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate this gate for me." Your computer replies with the follow: The function f (t) = a(sin (+4)) 6 models the position of an oscillating particle that has recently been discovered. Assume that a is a constant. What is the function that represents the velocity of this particle? Note: If you want to write a power of a trigonometric function, remember that writing sin(x) to the fourth power as sin () is just a shorthand method. To be mathematically correct, you should write that as (sin(x))4- which is what your computer expects and can translate. Velocity Function: