Questions: Find the amplitude and period of the function. y=cos(4πx) amplitude period Sketch the graph of the function.

Solution Steps

The amplitude of a cosine function \( y = a \cos(bx) \) is given by the absolute value of the coefficient \( a \). In this case, the function is \( y = \cos(4\pi x) \), where \( a = 1 \).

Since \( a = 1 \), the amplitude is: \[ \text{Amplitude} = |1| = 1 \]

The period of a cosine function \( y = a \cos(bx) \) is given by \( \frac{2\pi}{|b|} \). In this case, \( b = 4\pi \).

Using the formula for the period: \[ \text{Period} = \frac{2\pi}{|4\pi|} = \frac{2\pi}{4\pi} = \frac{1}{2} \]

Final Answer