Give the phase shift in radians (along x) of f (x) = sin (x - 3pi/5
To determine the phase shift of the function f(x) = sin(x - 3π/5), we need to compare the given function to the standard form of the sine function, which is f(x) = sin(x).
In the standard form, the phase shift is given by the horizontal shift of the graph. The general formula to find the phase shift is:
Phase shift = (horizontal shift) / (wavelength)
In this case, the horizontal shift is the value inside the sine function's argument, which is (x - 3π/5). The phase shift is typically reported in radians.
To find the phase shift, we compare the given function f(x) = sin(x - 3π/5) to the standard form f(x) = sin(x). We see that the argument of the sine function has been shifted by 3π/5 to the right (to the positive x-direction). Therefore, the phase shift is 3π/5 to the right.
Since the question asks for the phase shift in radians, we can conclude that the phase shift of f(x) = sin(x - 3π/5) is 3π/5 radians to the right.