Questions: Consider the function y(t)=-5+2 cos (πt/3) a) Find the period. 1. 3 2. 6 3. 3/π 4. 2 5. 6/π 6. None of these

Solution Steps

To find the period of the function \( y(t) = -5 + 2 \cos \left(\frac{\pi t}{3}\right) \), we need to determine the period of the cosine function inside it. The general form of a cosine function is \( \cos(bt) \), where the period is given by \( \frac{2\pi}{b} \). In this case, \( b = \frac{\pi}{3} \).

1. Identify the coefficient \( b \) inside the cosine function.
2. Use the formula for the period of a cosine function, \( \frac{2\pi}{b} \).

The function given is

\[ y(t) = -5 + 2 \cos \left(\frac{\pi t}{3}\right) \]

In this function, the coefficient \( b \) inside the cosine is

\[ b = \frac{\pi}{3} \]

The period \( T \) of a cosine function is calculated using the formula

\[ T = \frac{2\pi}{b} \]

Substituting the value of \( b \):

\[ T = \frac{2\pi}{\frac{\pi}{3}} = 2\pi \cdot \frac{3}{\pi} = 6 \]

Final Answer