Santiago Boone
10/07/2023 · High School
Determine the amplitude and period of the following function without graphing. \( y=-\frac{5}{7} \cos \left(\frac{7}{6} x\right) \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To determine the amplitude and period of the function \( y = -\frac{5}{7} \cos \left(\frac{7}{6} x\right) \), we can analyze the components of the cosine function.
1. **Amplitude**: The amplitude of a cosine function \( y = A \cos(Bx) \) is given by the absolute value of the coefficient \( A \). In this case, the coefficient is \( -\frac{5}{7} \). The amplitude is therefore:
\[
\text{Amplitude} = |A| = \left| -\frac{5}{7} \right| = \frac{5}{7}
\]
2. **Period**: The period of a cosine function \( y = A \cos(Bx) \) is calculated using the formula:
\[
\text{Period} = \frac{2\pi}{|B|}
\]
Here, \( B = \frac{7}{6} \). Thus, the period is:
\[
\text{Period} = \frac{2\pi}{\left| \frac{7}{6} \right|} = \frac{2\pi}{\frac{7}{6}} = 2\pi \cdot \frac{6}{7} = \frac{12\pi}{7}
\]
In summary, the amplitude and period of the function \( y = -\frac{5}{7} \cos \left(\frac{7}{6} x\right) \) are:
- Amplitude: \( \frac{5}{7} \)
- Period: \( \frac{12\pi}{7} \)
Quick Answer
Amplitude: \( \frac{5}{7} \), Period: \( \frac{12\pi}{7} \)
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
(0)
Ask Real Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
PREV 
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Uploaded Files
xxxx.png0%
Submit
