consider the function $y = \\cos(x+\frac{\\pi}{6})$. which of the following is true? there is a phase shift…

consider the function $y = \\cos(x+\frac{\\pi}{6})$. which of the following is true? there is a phase shift to the left. there is a phase shift to the right. the graph is reflected across the x - axis the graph is stretched horizontally. the graph is compressed horizontally. done

consider the function $y = \\cos(x+\frac{\\pi}{6})$. which of the following is true? there is a phase shift to the left. there is a phase shift to the right. the graph is reflected across the x - axis the graph is stretched horizontally. the graph is compressed horizontally. done

Answer

Explanation:

Step1: Recall cosine function transformation rule

For $y = \cos(x + c)$ where $c>0$, it represents a phase - shift.

Step2: Determine the direction of phase - shift

The general form of a cosine function is $y = A\cos(Bx - C)+D$. In the function $y=\cos(x+\frac{\pi}{6})$, comparing with the general form, we have $C =-\frac{\pi}{6}$. A positive value inside the cosine function's argument (in the form $x + c$) causes a left - hand shift. When we have $y=\cos(x+\frac{\pi}{6})$, it is equivalent to shifting the graph of $y = \cos(x)$ to the left by $\frac{\pi}{6}$ units.

Answer:

There is a phase shift to the left.