Questions: Which equation represents the graph? y=cos x-3 y=cos (x-3) y=sin x-3 y=sin (x-3)

Transcript text: Which equation represents the graph? $y=\cos x-3$ $y=\cos (x-3)$ $y=\sin x-3$ $y=\sin (x-3)$

Solution

Solution Steps

Step 1: Identify the type of trigonometric function

The graph shown is a cosine function because it starts at a maximum point when $ x = 0 $.

Step 2: Determine the phase shift

The graph appears to be shifted to the right. The standard cosine function $ y = \cos(x) $ starts at $ (0, 1) $, but this graph starts at $ (3, 1) $. This indicates a phase shift of 3 units to the right.

Step 3: Write the equation with the phase shift

The phase shift to the right by 3 units is represented by $ y = \cos(x - 3) $.

Final Answer

The equation that represents the graph is $ y = \cos(x - 3) $.

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