determine the amplitude and period of the following function without graphing. y = -\\frac{7}{9}\\cos(\\frac{…

determine the amplitude and period of the following function without graphing. y = -\\frac{7}{9}\\cos(\\frac{7}{6}x)\nfor the function given, the amplitude is \\frac{7}{9} (simplify your answer. type an exact answer, using pi as needed. use integers or fractions for any numbers in the expression.)\nfor the function given, \\omega = , so that the period = t = (simplify your answers. type exact answers, using pi as needed. use integers or fractions for any numbers in the expression.)

determine the amplitude and period of the following function without graphing. y = -\\frac{7}{9}\\cos(\\frac{7}{6}x)\nfor the function given, the amplitude is \\frac{7}{9} (simplify your answer. type an exact answer, using pi as needed. use integers or fractions for any numbers in the expression.)\nfor the function given, \\omega = , so that the period = t = (simplify your answers. type exact answers, using pi as needed. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Recall amplitude formula

For a cosine function of the form $y = A\cos(\omega x)$, the amplitude is $|A|$. In the function $y=-\frac{7}{9}\cos(\frac{7}{6}x)$, $A =-\frac{7}{9}$, so the amplitude is $\left|-\frac{7}{9}\right|=\frac{7}{9}$.

Step2: Identify the value of $\omega$

For the function $y =-\frac{7}{9}\cos(\frac{7}{6}x)$, comparing with $y = A\cos(\omega x)$, we have $\omega=\frac{7}{6}$.

Step3: Recall period formula

The period $T$ of a cosine function $y = A\cos(\omega x)$ is given by $T=\frac{2\pi}{\omega}$. Substituting $\omega=\frac{7}{6}$ into the formula, we get $T=\frac{2\pi}{\frac{7}{6}}$.

Step4: Calculate the period

$T = 2\pi\times\frac{6}{7}=\frac{12\pi}{7}$.

Answer:

For the function given, $\omega=\frac{7}{6}$, so that the period $T=\frac{12\pi}{7}$