# Trigonometric Derivatives

• Feb 29th 2008, 09:49 AM
mathlete
Trigonometric Derivatives
The voltage, V (in volts), in an electrical outlet is given as a function of time, t (in seconds), by the function V(t) = 156 cos(120πt).

(a) Find the rate of change of voltage with respect to time.
V '(t) =

ok so i found the rate of change, it is

-18720(pi)(sin(120pi(t))

now it wants to know the maximum value of the rate of change...can someone tell how to find it please..thanks

mathlete
• Feb 29th 2008, 10:39 AM
jayAndy
Possible Help, not sure
suppose V(t) = a Vehicles traveling on a plane

you have the equation for the position = V(t)
the first derivitive gives you velocity = V'(t)

I believe to need the second derivitive V''(t) (acceleration) where V''(t) = 0 in the positive direction, it's basically the max/min approach to Calculas.

Anyone help me if this is/is not correct.
• Feb 29th 2008, 11:03 AM
TheEmptySet
Quote:

Originally Posted by mathlete
The voltage, V (in volts), in an electrical outlet is given as a function of time, t (in seconds), by the function V(t) = 156 cos(120πt).

(a) Find the rate of change of voltage with respect to time.
V '(t) =

ok so i found the rate of change, it is

-18720(pi)(sin(120pi(t))

now it wants to know the maximum value of the rate of change...can someone tell how to find it please..thanks

ie take another derivative and find crit points ect...

mathlete

The max or min or any sine function is plus or minus 1. so the max value will be $-18720\pi$(-1)

or you could maximize the derivative using calculus if you want.