To identify the amplitude, period, and frequency of a trigonometric function, we typically need to analyze its form. Common forms include:
- \( y = A \sin(Bx) \) or \( y = A \cos(Bx) \)
- Amplitude \( |A| \)
- Period \( \frac{2\pi}{|B|} \)
- Frequency \( |B| \)
Based on the statements provided, we can analyze each one to determine its correctness:
-
The function has a period of \( \frac{\pi}{2} \):
- If the period is \( \frac{2\pi}{|B|} \), to have a period of \( \frac{\pi}{2} \), \( |B| \) would need to be 4 (since \( \frac{2\pi}{4} = \frac{\pi}{2} \)).
- This could be true depending on the value of \( B \).
-
The function has an amplitude of 5:
- This means \( |A| = 5 \). This could be true depending on the value of \( A \).
-
The function has an amplitude of 0:
- This means \( A = 0 \), which would result in a horizontal line (no oscillation). This is typically false for sine or cosine functions unless specifically stated.
-
The function has a frequency of \( \frac{3}{2\pi} \):
- Frequency is defined as \( |B| \), and since period is \( \frac{2\pi}{|B|} \), rearranging gives \( |B| = \frac{2\pi}{\text{Period}} \). If the frequency stated is \( \frac{3}{2\pi} \), that implies a period of \( \frac{2\pi}{\frac{3}{2\pi}} = \frac{4\pi^2}{3} \), which seems unlikely without context.
Without the actual graph, we cannot definitively determine which statement is correct. However, if we consider that a function typically cannot have an amplitude of 0 and exhibit oscillatory behavior, that statement is usually false.
Please check the graph for values of amplitude, period, and frequency based on the above definitions to clarify the correct choice amongst the responses listed. If you have the specific form of the function or any additional data, feel free to provide that for further assistance!
1 answer