Question

assignment 8.1: graphs of the sine and cosine functions
score: 1/21 answered: 1/10
question 2
which of the following graphs is the correct plot of ( y = 2 cos ( x ) )?

Explanation:

Step1: Recall the general form of cosine function

The general form of a cosine function is \(y = A\cos(x)\), where \(A\) is the amplitude.

Step2: Determine the amplitude

For the function \(y = 2\cos(x)\), the amplitude \(A = 2\). This means the maximum value of the function is \(2\) and the minimum value is \(- 2\).

Step3: Analyze the key points

The standard cosine function \(y=\cos(x)\) has a value of \(1\) at \(x = 0\). For \(y = 2\cos(x)\), when \(x = 0\), \(y=2\cos(0)=2\times1 = 2\).

Answer:

The graph with a maximum value of \(2\) and passing through the point \((0,2)\) is the correct plot of \(y = 2\cos(x)\)