Which of the following correctly describes the phase shift of the function f(x) = 2sin(x+π6)

Question

?(1 point)
Responses

π6
pi over 6

−π6
negative pi over 6

2

Answer 1

The phase shift of the function \( f(x) = 2 \sin(x + \frac{\pi}{6}) \) can be determined from the expression inside the sine function. In the general form of a sine function \( f(x) = a \sin(b(x - c)) + d \), the phase shift is given by \( c \), where \( c \) is derived from the equation \( x + \frac{\pi}{6} = 0 \).

To find \( c \):

1. Rewrite \( x + \frac{\pi}{6} \) as \( x - (-\frac{\pi}{6}) \).
2. This indicates that the phase shift is \( -\frac{\pi}{6} \).

Therefore, the correct response that describes the phase shift is:

−π/6 (negative pi over 6).