Answer :
To graph two full periods of the function \( f(x) = 6 \cos(TX) \), you can follow these steps:
1. Determine the period of the cosine function:
- The period of a cosine function is calculated using the formula \( T = \frac{2\pi}{|B|} \) where \( B \) is the coefficient of \( x \) inside the cosine function. In this case, \( B = T \). So, the period of the given function is \( T = \frac{2\pi}{T} \).
2. Calculate the period of the function:
- Since the period of the cosine function is \( 2\pi \), set \( \frac{2\pi}{T} = 2\pi \) and solve for \( T \) to find the value of \( T \).
3. Graphing two full periods of the function:
- Once you have determined the period \( T \), you can graph two full periods by plotting points on the graph. Remember that the cosine function oscillates between -1 and 1. Start by plotting key points like the maximum, minimum, and intercepts for two full periods based on the period you calculated.
By following these steps and plotting the points accurately, you will be able to graph two full periods of the function \( f(x) = 6 \cos(TX) \) effectively.
