What is the amplitude of g(x)=-9cos((pi)/(2)x-6)+8? units

Identify Amplitude Coefficient: The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine term. In the function g(x) = -9cos((pi)/(2)x - 6) + 8, the coefficient in front of the cosine term is -9.Calculate Absolute Value: To find the amplitude, we take the absolute value of -9, which is 9.Amplitude Determination: The amplitude does not depend on the horizontal shift (in this case, -6) or the vertical shift (in this case, +8). It is solely determined by the coefficient of the cosine term.Final Amplitude Calculation: Therefore, the amplitude of the function g(x) is 9 units.

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Math Problems

Grade 8

Solve equations with variables on both sides: fractional coefficients

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Q. What is the amplitude of

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g(x)=-9 \cos \left(\frac{\pi}{2} x-6\right)+8 ?

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units

Identify Amplitude Coefficient: The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine term. In the function $g(x) = -9\cos\left(\frac{\pi}{2}x - 6\right) + 8$ , the coefficient in front of the cosine term is $-9$ .
Calculate Absolute Value: To find the amplitude, we take the absolute value of $-9$ , which is $9$ .
Amplitude Determination: The amplitude does not depend on the horizontal shift (in this case, $-6$ ) or the vertical shift (in this case, $+8$ ). It is solely determined by the coefficient of the cosine term.
Final Amplitude Calculation: Therefore, the amplitude of the function $g(x)$ is $9$ units.