# What is the amplitude of #y=cos(-3x)# and how does the graph relate to #y=cosx#?

##### 1 Answer

**Exploring Graphs available:**

**Amplitude**

**Period**

#### Explanation:

The **Amplitude** is the **height** from the center line to the **peak** or to the **trough.**

Or, we can measure the **height** from the **highest to lowest points** and divide that value by

A **Periodic Function** is a function that **repeats** its values in **regular intervals** or **Periods.**

We can observe this behavior in the graphs available with this solution.

Note that the trigonometric function **Cos** is a **Periodic Function.**

We are given the trigonometric functions

The **General Form** of the equation of the **Cos** function:

**A** represents the **Vertical Stretch Factor** and its **absolute value** is the **Amplitude.**

**B** is used to find the **Period (P)**:

**C**, if given, indicates that we have a **place shift** BUT **it is NOT equal** to

The **Place Shift** is actually equal to

**D** represents **Vertical Shift**.

The trigonometric function available with us is

Observe the graph given below:

Observe the graph given below:

Combined Graphs of the trigonometric functions

are available below for establishing relationship:

How does the graph of

**Exploring the graphs above, we note that:**

**Amplitude**

**Period**

**We also note the following:**

the graph of **symmetric about the y-axis**, because it is an **Even** function.

the **domain** of each function is **range** is