2sec(3x-(pi/3))
Find the period.
when is 3 x = 2 pi ?
When does the period occur and the phase shift?
To find the period of the given function 2sec(3x-(π/3)), we can start by looking at the general formula for the period of the secant function.
The period of sec(x) is equal to 2π.
In the given function, we have 2sec(3x-(π/3)), which means the entire expression inside sec function, i.e., (3x-(π/3)), will complete one full cycle or period within the interval equal to the period of the sec(x) function, which is 2π.
So, we can set up an equation using the expression (3x-(π/3)):
3x - (π/3) = 2π
Now, let's solve for x.
Adding (π/3) to both sides:
3x = 2π + (π/3)
Now, combine the terms:
3x = (6π + π)/3
3x = (7π/3)
Dividing both sides by 3:
x = (7π/9)
Hence, the period of the given function 2sec(3x-(π/3)) is (7π/9).