Question
What are the amplitude and period of y=3 sin(-2x)
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Answers
GPT-4o mini
To determine the amplitude and period of the function \( y = 3 \sin(-2x) \), let's analyze the components of the sine function.
1. **Amplitude**: The amplitude of a sine function of the form \( y = A \sin(Bx) \) is given by the absolute value of \( A \). In this case, \( A = 3 \). Therefore, the amplitude is:
\[
\text{Amplitude} = |A| = |3| = 3
\]
2. **Period**: The period of a sine function is calculated using the formula \( \frac{2\pi}{|B|} \), where \( B \) is the coefficient of \( x \). In this case, since we have \( y = 3 \sin(-2x) \), the coefficient \( B = -2 \). The absolute value is taken to find the period:
\[
\text{Period} = \frac{2\pi}{|-2|} = \frac{2\pi}{2} = \pi
\]
In summary, for the function \( y = 3 \sin(-2x) \):
- The **amplitude** is \( 3 \).
- The **period** is \( \pi \).
1. **Amplitude**: The amplitude of a sine function of the form \( y = A \sin(Bx) \) is given by the absolute value of \( A \). In this case, \( A = 3 \). Therefore, the amplitude is:
\[
\text{Amplitude} = |A| = |3| = 3
\]
2. **Period**: The period of a sine function is calculated using the formula \( \frac{2\pi}{|B|} \), where \( B \) is the coefficient of \( x \). In this case, since we have \( y = 3 \sin(-2x) \), the coefficient \( B = -2 \). The absolute value is taken to find the period:
\[
\text{Period} = \frac{2\pi}{|-2|} = \frac{2\pi}{2} = \pi
\]
In summary, for the function \( y = 3 \sin(-2x) \):
- The **amplitude** is \( 3 \).
- The **period** is \( \pi \).