Transformation of the Sine function

Today in class, we learned what each parameter in the sine function does.

This is what a sine function formula looks like:



but.. what does the formula mean?

Let's start with Parameter D:

Parameter D shifts the graph up and down
- a (+) value shifts the graph upwards by
x number of units
- a (-) value shifts the graph downwards

so..if D = 2, the graph shifts up 2 units
if D = -2, it shifts down 2 units




Parameter A:


Parameter A controls the amplitude of
the graph

* The amplitude gets higher when the value of
gets bigger. A negative value will flip the wave
upside down, but the height of the wave does
not change.

Example:



-the black wave is what a basic
function looks like
- the blue wave represents the function with
a negative A value (A=-2)
-the red wave represents the function with a
positive A value (A= 2)

Parameter B:



Parameter controls the width of the
graph. It also multiplies the copy of
the wave.

normal sine function : period = 2π
so...B= 2 is the same as 2π/2 or π
* the value of B becomes divides the
normal sine function.

Example :



- black wave : sin(X)
- red wave : sin (2X)
Parameter C:



Parameter C shifts the graph
left and right
- a (+) value shifts the graph
to the left by x number of
units.
- a (-) value shifts the graph
to the right.

Example:


- black wave - represents the basic
sine function
- red wave - represents a positive C
value ( C=2)
- blue wave - represents a negative C
value (C= -2)

That's it for today's blog. I hope it helped you guys understand the today's topic.

The next blogger will be... Roe.