Question

Use the graph below to answer the question that follows:

What trigonometric function represents the graph?

 f(x) = −3 sin(x − )
f(x) = −3 cos(x − ) 
f(x) = 3 cos(x − )
f(x) = 3 sin(x − ) 

Answer 1

Let's start with our parent function:

f(x) = sin x

One cycle on this graph occurs between 0 and 2π. Therefore, our b-value is one.

There is no vertical shift up. The sinusoidal axis is along y = 0.

The wave is not inverted, it starts at the origin and rises on both the y and x axis. Thus there is no negative value before the function.

The amplitude of the wave is 3. A normal sine wave rises to a maximum of 1, but this is multiplied by 3.

f(x) = 3 sin x

There are an infinite amount of equations that could be used to represent this graph, but this is perhaps the most intuitive.