The amplitude is half the distance between the midline and the minimum point, which is 8.6 divided by 2. Therefore, the amplitude is 4.3.
Identify the Midline
From the information given, we know that the function intersects its midline at the point (3/5π, 4.2). This means the midline equation is y = 4.2.
Identify the Minimum Point
We also know that the function has a minimum point at the point (-2/5π, -4.4).
Calculate the Distance between the Midline and the Minimum Point
The distance between the midline (y = 4.2) and the minimum point (y = -4.4) is:
| Midline | y = 4.2 |
| Minimum point | y = -4.4 |
| Distance | |
Calculating the distance, we get:
| Distance | = |4.2 - (-4.4)| |
| | = |8.6| |
Therefore, the distance between the midline and the minimum point is 8.6.
Amplitude is Half the Distance
The amplitude of a trigonometric function is half the distance between the midline and the highest or lowest point of the graph. So, in this case:
| Amplitude | = 1/2 * Distance |
| | = 1/2 * 8.6 |
| | = 4.3 |
Therefore, the amplitude of the trigonometric function is **4.3**.
complete the question
Below is the graph of a trigonometric function. It intersects its midline at ( 3/5 π ,4.2) , and it has a minimum point at (- 2/5 π ,-4.4) What is the amplitude of the function?