Identify the amplitude, period, and phase shift, and graph the function. $$ y=\cos \left(3 x-\frac{\pi}{5}\right) $$

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Step 1: Identify the amplitude from the cosine function, which is the coefficient in front of the cosine. Here, it is 1.

Step 2: Determine the period using the formula $$\frac{2\pi}{b}$$, where $$b$$ is the coefficient of $$x$$. In this case, $$b = 3$$, so the period is $$\frac{2\pi}{3}$$.

Step 3: Calculate the phase shift using the formula $$\frac{c}{b}$$, where $$c$$ is the constant subtracted from $$x$$ in the argument of the cosine function. Here, $$c = \frac{\pi}{5}$$, so the phase shift is $$\frac{\frac{\pi}{5}}{3} = \frac{\pi}{15}$$.

Step 4: To graph the function, start by plotting the amplitude, period, and phase shift on the coordinate plane. The cosine function will start at its maximum value (1) at $$x = \frac{\pi}{15}$$ and will complete one full cycle by $$x = \frac{2\pi}{3} + \frac{\pi}{15}$$.Amplitude: 1 Period: $$\frac{2\pi}{3}$$ Phase Shift: $$\frac{\pi}{15}$$

Identify the amplitude, period, and phase shift, and graph the function. \[ y=\cos \left(3 x-\frac{\pi}{5}\right) \]

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