y=2tan(x-1)
Find the period and phase shift.
remember that the period of tan kØ = π/k
whereas the period of sin kØ and cos kØ is 2π/k
so period of 2tan(x-1) is π
and the phase shift is 1 radian to the right
To find the period and phase shift of the given function, we need to understand the general form of a tangent function.
The general equation for a tangent function is y = A * tan(B(x - C)) + D, where A, B, C, and D are constants.
In this case, the given function is y = 2tan(x-1), which can be written in the general form as y = 2 * tan(1(x - 1)) + 0.
By comparing the given function with the general form, we can determine the values of A, B, C, and D.
A = 2, B = 1, C = 1, and D = 0.
Now, let's find the period and phase shift using these values.
1. Period:
The period of a tangent function is given by the formula: π/B.
In this case, B = 1, so the period is π/1 = π.
Therefore, the period of the function is π.
2. Phase Shift:
The phase shift of a tangent function is given by the formula: C/B.
In this case, C = 1 and B = 1, so the phase shift is 1/1 = 1.
Therefore, the phase shift of the function is 1.
To summarize:
- The period of the function y = 2tan(x-1) is π.
- The phase shift of the function y = 2tan(x-1) is 1.