Question

how do you find a sinusoidal function?

Answer 1

Sketch the graph of y=2sinxy=2sin⁡x from x=0x=0 to x=2πx=2π.

what to notice about the graph
Notice that this graph is twice as tall as the sine graph. The amplitude of a sinusoidal function is the distance from the midline of the graph to the highest point of the graph., the amplitude is (2\).


Sketch the graph of y=sin(x–π)y=sin⁡(x–π) from x=0x=0 to x=2πx=2π. You’ll have to shift the graph of y=sinxy=sin⁡x to the right by ππ units. In this case, ππ is called the phase shift of the function.



Sketch the graph of y=sin(2x)y=sin⁡(2x) from x=0x=0 to x=2πx=2π. You’ll have to compress the graph of y=sinxy=sin⁡x by one-half horizontally. This changes the period from 2π2π to 2π/22π/2. So this sinusoidal function has a period of ππ. To draw the graph from x=0x=0 to x=2πx=2π you’ll have to draw two complete cycles of the graph.



Sketch the graph of y=1+sinxy=1+sin⁡x from x=0x=0 to x=2πx=2π.

the general sinusoidal function
As you see, y=1+sinxy=1+sin⁡x merely raises the graph of sine one unit. We say that this sinusoidal has a vertical shift of 1.

In general, all of these types of alterations may occur in a sinusoidal function. The general form of a sinusoidal is:

f(x)=asin(bx–c)+d, for b>0
f(x)=asin⁡(bx–c)+d, for b>0
The following formulas will be useful:

Amplitude =|a|=|a|
Period =2π/b=2π/b
Phase shift =c/b=c/b
Vertical shift =d=d
Two complete cycles of the graph may be drawn between x=c/b–2π/bx=c/b–2π/b and x=c/b+2π/bx=c/b+2π/b.

But what if b is not positive?

Suppose f(x)=3sin(−2x+π/2)+3f(x)=3sin⁡(−2x+π/2)+3, for example. What do we do?

We replace sin(−2x+π/2)sin⁡(−2x+π/2) with −sin(2x−π/2)−sin⁡(2x−π/2) ! We can do this because, remember, sine is an odd function. This means that sin(−x)=−sin(x)sin⁡(−x)=−sin⁡(x) for all xx in the domain of the function.

Thus, f(x)=−3sin(2x−π/2)+3f(x)=−3sin⁡(2x−π/2)+3.


Sketch two complete cycles of the graph of f(x)=−3sin(2x−π/2)+3f(x)=−3sin⁡(2x−π/2)+3.

Specify the amplitude, vertical shift, period and phase shift.

Answer 2

were did you copy and paste from

Answer 3

i did most myself but gotsome of it from enotes.com

Answer 4

-_- really?
"Sketch the graph of y=2sinxy=2sin⁡x from x=0x=0 to x=2πx=2π."
I GAVE YOU NO GRAPH

Answer 5

yeah but no graph is needed if you go to enotes.com it gives some information but then you need to find the rest of it yourself which is easy when you used the site that will explain some of the concepts

Answer 6

i may be in highschool but im on my collage credits and im only a sophmore

Answer 7

honey im graduating high school this year with my bachelors. dont brag. you look stupid. i KNOW you didnt do any of that. I want to understand how to get the function with the example that I gave.

Answer 8

i did but nice try and im a guy not your honey bro

Answer 9

lol i call everyone honey. and I can tell you copied and pasted. sorry for wanting to LEARN what im doing. \_(o.0)_/

Answer 10

Grandson i did copy and paste but you also need to know that people can do things with some help and i needed help ill give you that im not trying to be a wingspan i did most work after i looked at the help to see what i was getting into

Answer 11

okay but like you didnt get help, you JUST copied and pasted.

Answer 12

I want to learn what im doing; because the test for this could fail my class. -_- i really want to pass it.

Answer 13

ok i get that im smart your smart we can talk about this