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7) y= -10c0s(%6) amplitude= period= phase shift= vertinal shift=

7) y= -10c0s(%6) amplitude= period= phase shift= vertinal shift=

Trigonometry (11th Edition)
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°.
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Find terms with equation
The given function is \( y = -10 \cos \left( \frac{x}{6} \right) \). ### Analyzing the Function 1. **Amplitude:** - The amplitude of a cosine function in the form \( y = a \cos(bx) \) is the absolute value of \( a \). Here, the amplitude is \(|-10| = 10\). 2. **Period:** - The period of a function in the form \( y = a \cos(bx) \) is given by \(\frac{2\pi}{b}\). Here, \( b = \frac{1}{6} \), so the period is \(\frac{2\pi}{\frac{1}{6}} = 12\pi\). 3. **Phase Shift:** - A phase shift occurs if there is a horizontal shift inside the cosine function. The standard form is \( y = a \cos(bx - c) \). Here, there is no \(c\), so the phase shift is 0. 4. **Vertical Shift:** - The vertical shift occurs if there's a constant added or subtracted from the function \( y = a \cos(bx) + d \). Here, \( d = 0 \), so the vertical shift is 0. This analysis is critical for understanding how the graph of the function will behave and transform.
Transcribed Image Text:The given function is \( y = -10 \cos \left( \frac{x}{6} \right) \). ### Analyzing the Function 1. **Amplitude:** - The amplitude of a cosine function in the form \( y = a \cos(bx) \) is the absolute value of \( a \). Here, the amplitude is \(|-10| = 10\). 2. **Period:** - The period of a function in the form \( y = a \cos(bx) \) is given by \(\frac{2\pi}{b}\). Here, \( b = \frac{1}{6} \), so the period is \(\frac{2\pi}{\frac{1}{6}} = 12\pi\). 3. **Phase Shift:** - A phase shift occurs if there is a horizontal shift inside the cosine function. The standard form is \( y = a \cos(bx - c) \). Here, there is no \(c\), so the phase shift is 0. 4. **Vertical Shift:** - The vertical shift occurs if there's a constant added or subtracted from the function \( y = a \cos(bx) + d \). Here, \( d = 0 \), so the vertical shift is 0. This analysis is critical for understanding how the graph of the function will behave and transform.
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