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**Find the specified quantity.** **Explain the transformation of the amplitude.** Find the amplitude of \( y = -2 \sin \left( x + \frac{\pi}{2} \right) - 3 \). **Explanation:** - The given function is \( y = -2 \sin \left( x + \frac{\pi}{2} \right) - 3 \). - The amplitude of a sine function \( y = a \sin(bx + c) + d \) is the absolute value of \( a \). - In this case, \( a = -2 \), so the amplitude is \( |a| = 2 \). - The negative sign indicates a reflection over the x-axis, but it does not affect the amplitude value.

**Find the specified quantity.** **Explain the transformation of the amplitude.** Find the amplitude of \( y = -2 \sin \left( x + \frac{\pi}{2} \right) - 3 \). **Explanation:** - The given function is \( y = -2 \sin \left( x + \frac{\pi}{2} \right) - 3 \). - The amplitude of a sine function \( y = a \sin(bx + c) + d \) is the absolute value of \( a \). - In this case, \( a = -2 \), so the amplitude is \( |a| = 2 \). - The negative sign indicates a reflection over the x-axis, but it does not affect the amplitude value.

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 the specified quantity.** **Explain the transformation of the amplitude.** Find the amplitude of \( y = -2 \sin \left( x + \frac{\pi}{2} \right) - 3 \). **Explanation:** - The given function is \( y = -2 \sin \left( x + \frac{\pi}{2} \right) - 3 \). - The amplitude of a sine function \( y = a \sin(bx + c) + d \) is the absolute value of \( a \). - In this case, \( a = -2 \), so the amplitude is \( |a| = 2 \). - The negative sign indicates a reflection over the x-axis, but it does not affect the amplitude value.
Transcribed Image Text:**Find the specified quantity.** **Explain the transformation of the amplitude.** Find the amplitude of \( y = -2 \sin \left( x + \frac{\pi}{2} \right) - 3 \). **Explanation:** - The given function is \( y = -2 \sin \left( x + \frac{\pi}{2} \right) - 3 \). - The amplitude of a sine function \( y = a \sin(bx + c) + d \) is the absolute value of \( a \). - In this case, \( a = -2 \), so the amplitude is \( |a| = 2 \). - The negative sign indicates a reflection over the x-axis, but it does not affect the amplitude value.
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