Question

3 find the phase shift and vertical shift of the cosine graph
phase shift
vertical shift

Explanation:

Step1: Recall the general form of a sinusoidal function

The general form of a sinusoidal function is \(y = A\sin(B(x - C))+D\) or \(y = A\cos(B(x - C))+D\). The phase - shift is given by \(C\) (if \(C>0\), shift to the right; if \(C < 0\), shift to the left) and the vertical shift is given by \(D\).

Step2: Analyze the graph for phase - shift

The graph passes through the origin \((0,0)\) and there is no horizontal displacement from the standard sine or cosine function (assuming a basic starting point). So, the phase - shift \(C = 0\).

Step3: Analyze the graph for vertical - shift

The mid - line of the graph is \(y = 0\). For a sinusoidal function \(y=A\sin(Bx)+D\) or \(y = A\cos(Bx)+D\), the mid - line is \(y = D\). So, the vertical shift \(D=0\).

Answer:

Phase Shift: \(0\), Vertical Shift: \(0\)