Rewrite - 1 sin(z) - 6 cos(z) as A sin(z + 4) A= VT =| 80.53767779 Note: 6 should be in the interval -T<6
Rewrite - 1 sin(z) - 6 cos(z) as A sin(z + 4) A= VT =| 80.53767779 Note: 6 should be in the interval -T<6
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
![**Trigonometric Function Transformation**
To rewrite the trigonometric function \( -1 \sin(x) - 6 \cos(x) \) in the form \( A \sin(x + \phi) \), follow these steps:
1. **Determine the Amplitude, \( A \):**
- Calculate \( A \) using the formula:
\[
A = \sqrt{(-1)^2 + (-6)^2} = \sqrt{37}
\]
- The value of \( A \) is \( \sqrt{37} \), as shown by the checkmark indicating correctness.
2. **Find the Phase Shift, \( \phi \):**
- The incorrect calculation for \( \phi \) is shown as \( 80.53767779 \).
- Remember, the phase \(\phi\) should be within the interval:
\[
-\pi < \phi < \pi
\]
**Note:**
When calculating \( \phi \), ensure it lies within the specified interval for correctness in trigonometric transformations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7d5bf39-439e-4459-9b20-3ea6c61a83bb%2F1d3aca52-4ca4-44af-be92-8c945cfce468%2Fl5b1vm_processed.png&w=3840&q=75)
Transcribed Image Text:**Trigonometric Function Transformation**
To rewrite the trigonometric function \( -1 \sin(x) - 6 \cos(x) \) in the form \( A \sin(x + \phi) \), follow these steps:
1. **Determine the Amplitude, \( A \):**
- Calculate \( A \) using the formula:
\[
A = \sqrt{(-1)^2 + (-6)^2} = \sqrt{37}
\]
- The value of \( A \) is \( \sqrt{37} \), as shown by the checkmark indicating correctness.
2. **Find the Phase Shift, \( \phi \):**
- The incorrect calculation for \( \phi \) is shown as \( 80.53767779 \).
- Remember, the phase \(\phi\) should be within the interval:
\[
-\pi < \phi < \pi
\]
**Note:**
When calculating \( \phi \), ensure it lies within the specified interval for correctness in trigonometric transformations.
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