# How do you write the equation of a cos function: amplitude=2/3 period=pi/3 phase shift= -pi/3 vert. shift= 5?

##### 2 Answers

#### Answer:

Start with the general form:

Please see the explanation for how you change it.

#### Explanation:

A is the amplitude:

The period is

Substitute

The phase shift is

Substitute,

The vertical shift is

Here is a graph of the above equation:

graph{y = 2/3cos(6x + 2pi) + 5 [-11.25, 11.25, -5.625, 5.625]}

#### Answer:

#### Explanation:

let's write out something really general first

Easy ones first:

Amplitude:

Vertical Shift upward:

Ergo:

For the period (am assuming you mean temporal, not spatial, period, though the approach is the same), note that

For phase shift

We want that shift to be

ie we can say that

That may seem odd but the period of the function is