Fill in the blanks to correctly complete the sentence below.

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Part 1

The graph of 

yequals=cosine left parenthesis x minus StartFraction pi Over 2 EndFraction right parenthesiscosx−π2 

is obtained by shifting the graph of 

yequals=cosine xcosx 

enter your response here 

​unit(s) to the 

right.

To correctly complete the sentence:

The graph of \( y = \cos\left( x - \frac{\pi}{2} \right) \) is obtained by shifting the graph of \( y = \cos(x) \) **\(\frac{\pi}{2}\)** units to the **right**.

### Explanation:
When you have a function \( y = \cos(x - h) \), the graph of the cosine function shifts horizontally by \( h \) units. If \( h \) is positive (as in \( x - \frac{\pi}{2} \)), the graph shifts **right**. If it were \( x + h \), it would shift left.

In this case, since it’s \( x - \frac{\pi}{2} \), the shift is **\(\frac{\pi}{2}\)** units to the right. 

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Would you like further details or explanations on shifts in trigonometric graphs?

### 5 Related Questions:
1. What happens to the graph of \( \sin(x) \) if we shift it by \( \pi/2 \) units to the left?
2. How does the amplitude of the cosine function change with coefficients like \( A \cdot \cos(x) \)?
3. What is the effect of a vertical shift on \( \cos(x) \)?
4. How can we express the phase shift of \( y = \cos(x - \pi/3) \)?
5. What is the period of a general cosine function \( y = \cos(Bx - C) \)?

### Tip:
Horizontal shifts are always applied in the opposite direction of what they appear: \( (x - h) \) shifts right, while \( (x + h) \) shifts left!

Fill in the blanks to correctly complete the sentence below.
The graph of y = cos(x - π/2) is obtained by shifting the graph of y = cos(x) ___ unit(s) to the right.

Learn how the graph of y = cos(x) shifts horizontally to become y = cos(x - π/2). This problem covers key trigonometric concepts such as horizontal shifts and transformations of the cosine function, ideal for students in Grades 10-12.

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