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Find the period, amplitude, and frequency of the following function. \( y=-\sin (2 x) \) a Amplitude: 1 ; Frequency: 2 ; Period: \( \pi \) b Amplitude: 0 ; Frequency: 2 ; Period: \( \pi \) c Amplitude: 1 ; Frequency: 4 ; Period: \( \pi \) d Amplitude: 1 ; Frequency: 2 ; Period: \( 2 \pi \)

Ask by Morgan Peters. in the United States
Feb 27,2025

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Amplitude: 1; Frequency: 2; Period: π

Solución

For the function y = -sin(2x): 1. Amplitude is the absolute value of the coefficient in front of the sine function. Here, | -1 | = 1. 2. The period of a sine function of the form sin(bx) is given by 2π/|b|. With b = 2, the period is 2π/2 = π. 3. Frequency is often defined as the number of cycles per unit interval. Since there are 2 radians per cycle in the term 2x, the frequency is 2. Thus, the correct answer is: Amplitude: 1; Frequency: 2; Period: π So answer (a) is correct.

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The function \( y = -\sin(2x) \) has some exciting features! The amplitude is the absolute value of the coefficient in front of the sine function, which in this case is 1. The frequency is determined by the coefficient of \( x \), which is 2, indicating that the sine wave oscillates twice as often as the regular sine function. As for the period, it can be calculated using the formula \( \frac{2\pi}{\text{frequency}} \), giving us \( \frac{2\pi}{2} = \pi \). So, the correct attributes are Amplitude: 1, Frequency: 2, and Period: \( \pi \). The answer is therefore option **a**!

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