Questions: Without graphing the function, determine its amplitude or period as requested. y=-3 cos 1/2 x Find the period. 4 pi pi/2 3 pi/2 -3

Solution Steps

To find the period of the cosine function given by \( y = -3 \cos \frac{1}{2} x \), we need to identify the coefficient of \( x \) inside the cosine function. The general form of a cosine function is \( y = a \cos(bx + c) + d \), where the period is given by \( \frac{2\pi}{|b|} \). In this case, \( b = \frac{1}{2} \).

The given function is \( y = -3 \cos \frac{1}{2} x \). In this function, the coefficient of \( x \) is \( b = \frac{1}{2} \).

The period \( P \) of a cosine function is calculated using the formula: \[ P = \frac{2\pi}{|b|} \] Substituting \( b = \frac{1}{2} \): \[ P = \frac{2\pi}{\frac{1}{2}} = 2\pi \cdot 2 = 4\pi \]

Final Answer