g(x)=-sin X- 元一4
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![**Function Analysis**
Given the function:
\[ g(x) = -\sin\left(x - \frac{\pi}{4}\right) \]
**Amplitude:**
The amplitude of a sinusoidal function \( a \sin(bx + c) \) or \( a \cos(bx + c) \) is the absolute value of \( a \).
**Equation of Mid-line:**
The mid-line is the horizontal line that runs through the middle of the maximum and minimum values of the function. For sine and cosine functions, the mid-line is \( y = d \) where \( d \) is the vertical shift.
**Length of Period:**
The period of the sine function \( \sin(bx + c) \) is calculated as \( \frac{2\pi}{|b|} \).
**Phase Shift:**
The phase shift is the horizontal shift of the function, calculated as \( -\frac{c}{b} \).
By analyzing this function, one can determine the characteristics based on the parameters provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F446d612d-b997-4951-bf61-55214d1953ff%2Fa7d26e53-0327-408b-9090-d8c15e3e7abc%2Fl8lm2xs.jpeg&w=3840&q=75)
Transcribed Image Text:**Function Analysis**
Given the function:
\[ g(x) = -\sin\left(x - \frac{\pi}{4}\right) \]
**Amplitude:**
The amplitude of a sinusoidal function \( a \sin(bx + c) \) or \( a \cos(bx + c) \) is the absolute value of \( a \).
**Equation of Mid-line:**
The mid-line is the horizontal line that runs through the middle of the maximum and minimum values of the function. For sine and cosine functions, the mid-line is \( y = d \) where \( d \) is the vertical shift.
**Length of Period:**
The period of the sine function \( \sin(bx + c) \) is calculated as \( \frac{2\pi}{|b|} \).
**Phase Shift:**
The phase shift is the horizontal shift of the function, calculated as \( -\frac{c}{b} \).
By analyzing this function, one can determine the characteristics based on the parameters provided.
Expert Solution
Step 1
Let us first plot the graph of the following.
From the above graph, we see the following.
amplitude = 1,
equation of mid-line = y=0.
Step by step
Solved in 2 steps with 2 images
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