determine the amplitude, period, and phase shift of the function. graph the function.\n$y =…

determine the amplitude, period, and phase shift of the function. graph the function.\n$y = \\frac{1}{2}\\cos\\left(3x + \\frac{\\pi}{2}\\right)$\nthe amplitude is $\\frac{1}{2}$.\n(simplify your answer.)\nthe period is $\\frac{2\\pi}{3}$.\n(type an exact answer, using $\\pi$ as needed. use integers or fractions for any numbers in the expression.)\nthe phase shift is \n(type an exact answer, using $\\pi$ as needed. use integers or fractions for any numbers in the expression.)\nuse the graphing tool to graph the function.\nclick to enlarge

determine the amplitude, period, and phase shift of the function. graph the function.\n$y = \\frac{1}{2}\\cos\\left(3x + \\frac{\\pi}{2}\\right)$\nthe amplitude is $\\frac{1}{2}$.\n(simplify your answer.)\nthe period is $\\frac{2\\pi}{3}$.\n(type an exact answer, using $\\pi$ as needed. use integers or fractions for any numbers in the expression.)\nthe phase shift is \n(type an exact answer, using $\\pi$ as needed. use integers or fractions for any numbers in the expression.)\nuse the graphing tool to graph the function.\nclick to enlarge

Answer

Explanation:

Step1: Recall the formula for phase shift

For a function (y = A\cos(Bx - C)+D), the phase shift is (\frac{C}{B}). First, rewrite (y=\frac{1}{2}\cos(3x+\frac{\pi}{2})) as (y=\frac{1}{2}\cos\left(3x-\left(-\frac{\pi}{2}\right)\right)). Here (B = 3) and (C=-\frac{\pi}{2}).

Step2: Calculate the phase shift

Using the formula (\text{Phase Shift}=\frac{C}{B}), substitute (B = 3) and (C =-\frac{\pi}{2}). (\text{Phase Shift}=\frac{-\frac{\pi}{2}}{3}=-\frac{\pi}{6})

Answer:

The phase shift is (-\frac{\pi}{6})