Question

Consider the function y = cos (x + pi/6). Which of the following is true?

Answer 1

The answer would be A. There is a phase shift to the left. Because you are adding pi/6.

Answer 2

Answer with explanation:

To Answer this question,

→→We will look at the graph and observe the function carefully

     y = cos x

It has domain equal to $[\frac{-\pi}{2}, \frac{-\pi}{2}]$

and Range equal to , [-1, 1].

On , Y axis it takes maximum value =1 at , x=0 degree.

And→→ when you will look at the graph and observe the second  function,

 $y=cos (x +\frac{\pi}{6})$

Domain is equal to $[\frac{-\pi}{2}+\frac{\pi}{6} ,\frac{\pi}{2}+\frac{\pi}{6}]=[\frac{-\pi}{3},\frac{2\pi}{3}]$

Range =[-1, 1]

It's Maximum value is also =1, which it takes at , x=-30 degree.

And, when you will compare the graphs of two functions,the graph has been shifted

  $\frac{\pi}{2} - \frac{\pi}{3}=\frac{\pi}{6}$

to the left.

Option A: There is a phase shift to the left.