Select all the correct locations on the graph. The graph of a cosine function is shown. Which two points on the midline of the function are separated by a distance of one period? 2,5 2- 1.5- 1- 0.5- 8 8 2 8
Select all the correct locations on the graph. The graph of a cosine function is shown. Which two points on the midline of the function are separated by a distance of one period? 2,5 2- 1.5- 1- 0.5- 8 8 2 8
Select all the correct locations on the graph. The graph of a cosine function is shown. Which two points on the midline of the function are separated by a distance of one period? 2,5 2- 1.5- 1- 0.5- 8 8 2 8
Transcribed Image Text:**Cosine Function Graph Analysis**
**Instructions:**
Select all the correct locations on the graph.
**Problem Statement:**
The graph of a cosine function is shown. Which two points on the midline of the function are separated by a distance of one period?
**Graph Explanation:**
- **Axes:**
- The vertical axis is labeled \( y \).
- The horizontal axis is labeled \( x \).
- **Cosine Curve:**
- The graph displays a wave-like pattern characteristic of the cosine function.
- The amplitude of the cosine wave reaches a maximum of \( y = 2.5 \) and a minimum of \( y = -0.5 \).
- **Points of Interest:**
- Several points are highlighted along the cosine curve. These points indicate key locations at regular intervals.
- **Highlighted Points:**
- These points are located at:
- \(( \frac{\pi}{4}, 2.5)\)
- \(( \frac{3\pi}{4}, -0.5)\)
- \(( \frac{\pi}{2}, 2.5)\)
- \(( \pi, -0.5)\)
- \(( \frac{3\pi}{2}, 2.5)\)
- \(( \frac{5\pi}{4}, 0)\)
- These points help identify specific locations corresponding to the cosine function as it moves through its period.
- **Period Identification:**
- In a typical cosine function, a period is defined as the interval after which the function repeats its values.
- By examining the highlighted points, we look for two points on the midline (average value) that are separated by exactly one period.
**Graph Features:**
- There are 'Reset' and 'Next' buttons below the graph for user interaction.
**Conclusion:**
To solve the problem, identify the midline as the average value of the function, and then find two points along this line that are separated by a distance equivalent to one period of the cosine function.
**Interactive Components:**
- **Reset Button:** Allows users to reset their selections on the graph.
- **Next Button:** Proceeds to the next question or instructional step.
Feel free to interact with the graph to better understand the cosine wave and its characteristic period.
Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.
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