# What can you say about the shape of the curve # f(x) = 7 cos( 1/3 x ) + \sqrt{19} sin( 1/3 x ) # ?

##### 1 Answer

The graph of **sine wave**, also called a sinusoid.

#### Explanation:

A sine wave is described by the function

where

We ask; how can we turn our function into this form? Well, notice how our function is of the form

Where

As there is no constant term in the formula for

Square both relations and add them to reach the condition:

Dividing the second relation by the first yields

Hence

#=sqrt((sqrt19)^2+(7)^2)sin(1/3x + arctan 7"/"sqrt19)#

#=sqrt68sin(1/3x+arctan7"/"sqrt19)#

Proving that