The amplitude, period, and range of the function y = 6sin(6x + π/7) - 3 can be found as follows:

1. Amplitude: The amplitude of a sine function is the absolute value of the coefficient of the sine term. In this case, the coefficient is 6, so the amplitude is |6| = 6.

2. Period: The period of a sine function is determined by the coefficient of x inside the sine function. The general formula for the period is 2π/|B|, where B is the coefficient of x. In this case, B is 6, so the period is 2π/|6| = π/3.

3. Range: The range of a sine function is determined by the amplitude and the vertical shift (the constant term). The range will be [vertical shift - amplitude, vertical shift + amplitude]. In this case, the vertical shift is -3 and the amplitude is 6, so the range is [-3 - 6, -3 + 6] = [-9, 3].

So, the amplitude is 6, the period is π/3, and the range is [-9, 3].

Question

The amplitude, period, and range of the function y = 6sin(6x + π/7) - 3 can be found as follows:

1. Amplitude: The amplitude of a sine function is the absolute value of the coefficient of the sine term. In this case, the coefficient is 6, so the amplitude is |6| = 6.

2. Period: The period of a sine function is determined by the coefficient of x inside the sine function. The general formula for the period is 2π/|B|, where B is the coefficient of x. In this case, B is 6, so the period is 2π/|6| = π/3.

3. Range: The range of a sine function is determined by the amplitude and the vertical shift (the constant term). The range will be [vertical shift - amplitude, vertical shift + amplitude]. In this case, the vertical shift is -3 and the amplitude is 6, so the range is [-3 - 6, -3 + 6] = [-9, 3].

So, the amplitude is 6, the period is π/3, and the range is [-9, 3].

Knowee AI · Accepted Answer

The amplitude, period, and range of the function y = 6sin(6x + π/7) - 3 can be found as follows:

1. Amplitude: The amplitude of a sine function is the absolute value of the coefficient of the sine term. In this case, the coefficient is 6, so the amplitude is |6| = 6.

2. Period: The period of a sine function is determined by the coefficient of x inside the sine function. The general formula for the period is 2π/|B|, where B is the coefficient of x. In this case, B is 6, so the period is 2π/|6| = π/3.

3. Range: The range of a sine function is determined by the amplitude and the vertical shift (the constant term). The range will be [vertical shift - amplitude, vertical shift + amplitude]. In this case, the vertical shift is -3 and the amplitude is 6, so the range is [-3 - 6, -3 + 6] = [-9, 3].

So, the amplitude is 6, the period is π/3, and the range is [-9, 3].

Find the amplitude, period and range of 𝑦=6sin(6𝑥+𝜋7)−3

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