Sketch the graph of the given equation over the interval 

​[minus−2piπ​, 

2piπ​].

yequals=Bold cos**cos**left parenthesis x minus StartFraction pi Over 12 EndFraction right parenthesisx−π12


show me work

The graph of the function \( y = \cos \left( x - \frac{\pi}{12} \right) \) is shown above. It depicts the cosine wave, shifted to the right by \( \frac{\pi}{12} \), over the interval \([-2\pi, 2\pi]\). The wave maintains its typical oscillation between 1 and -1, with critical points shifted accordingly.

Let me know if you need any clarifications or further details!

Here are 5 related questions you can explore:
1. How would the graph change if the function was \( y = \cos(x + \frac{\pi}{12}) \)?
2. What effect does modifying the amplitude have on the cosine function?
3. How would the period of the function change if it was \( y = \cos(2x) \)?
4. Can you describe the graph of \( y = \sin\left( x - \frac{\pi}{12} \right) \)?
5. What happens to the graph if we introduce a vertical shift, such as \( y = \cos\left( x - \frac{\pi}{12} \right) + 1 \)?

**Tip:** The phase shift affects the horizontal position of the wave but does not alter the amplitude or period.

Sketch the graph of the given equation over the interval [−2π, 2π]. y = cos(x − π/12). Show me the work.

Learn how to sketch the graph of y = cos(x - π/12) over the interval [-2π, 2π]. This trigonometry problem explores phase shifts and key properties of the cosine function. Suitable for high school students in Grades 10-12.

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