Answer:
![f(x)=3*cosine(x)](https://tex.z-dn.net/?f=f%28x%29%3D3%2Acosine%28x%29)
Step-by-step explanation:
We are looking for a trigonometric function which contains the point (0, 3), and has an amplitude of 3.
We know that for a sine function
,
; therefore the function we a looking for cannot be a sine function because it is zero at
.
However, the cosine function
gives non-zero value at ![x=0:](https://tex.z-dn.net/?f=x%3D0%3A)
![f(0)=cos(0)=1](https://tex.z-dn.net/?f=f%280%29%3Dcos%280%29%3D1)
therefore, a cosine function can be our function.
Now, cosine function with amplitude
has the form
![f(x)=a*cos(x)](https://tex.z-dn.net/?f=f%28x%29%3Da%2Acos%28x%29)
this is because the cosine function is maximum at
and therefore, has the property that
![f(0)=a*cos(0)= a](https://tex.z-dn.net/?f=f%280%29%3Da%2Acos%280%29%3D%20a)
in other words it contains the point
.
The function we are looking for contains the point
; therefore, its amplitude must be 3, or
![f(x)=3cos(x)](https://tex.z-dn.net/?f=f%28x%29%3D3cos%28x%29)
we see that this function satisfies our conditions:
has amplitude of 3, and it passes through the point (0, 3) because ![f(0)=3](https://tex.z-dn.net/?f=f%280%29%3D3)