What is the period and amplitude of y=3tan(2/3x-pi/6)?
Thanks!
I do not think amplitude means much for a tangent function which goes to infinity twice a period so I would not say 3 but maybe undefined.
when the x term increases to 2 pi from 0 we have gone a period so
(2/3) x = 2 pi
x = 3 pi when we have gone a period
period = 3 pi
Sorry
tangent period is pi, not 2 pi so
(2/3) x = 1 pi
x = 3 pi/2 = period
To find the period and amplitude of the given function y = 3tan(2/3x - pi/6), we can start by determining the transformations applied to the basic tangent function y = tan(x).
The general form of the tangent function is given by y = A * tan(Bx - C), where A, B, and C are constants.
1. Period:
The period of the function is the distance it takes for one complete cycle or wave. For the tangent function, the period is given by the formula: P = π/B.
In our equation, B = 2/3, so the period (P) is equal to π divided by 2/3:
P = π / (2/3)
P = π * 3/2
P = 3π/2
2. Amplitude:
The amplitude of the tangent function represents the maximum vertical distance between the curve and its midline. However, the tangent function does not have a well-defined amplitude. Instead, it has vertical asymptotes at regular intervals.
Therefore, in the given equation, y = 3tan(2/3x - π/6), the number 3 in front of the tangent function does not represent the amplitude but rather a vertical scaling factor. It scales the tangent function vertically by a factor of 3.
To summarize:
- The period of y = 3tan(2/3x - π/6) is 3π/2.
- The function does not have a well-defined amplitude because the tangent function has vertical asymptotes.
I hope this explanation helps! Let me know if you have any further questions.