Math Help: Understanding Sinusoids

[Mona]

I do not understand how to find the period of a sinusoid. I don't know when I should use degrees or just numbers. I don't understand when there is a graph that looks the same yet the answers come out with degrees such as y=2sin(fada+45degrees) and another will come out y=10+2sin4fada.

 

[berkeman]

Have you learned about how to use either degrees or radians to express angles? That may be what is confusing you. Just remember that there are 2 * PI radians or 360 degrees in a complete circle. Here is an article about the sine function that may also help:

http://en.wikipedia.org/wiki/Sine

 

[cristo]

These graphs may look similar, but they are not the same! The general equation for a sine graph is y=Asin(Bx+C)+D. Here's, a site I found a while ago that has an "interactive tutorial." You can put in different values for each of A,B,C,D and see what the graph will look like.

http://www.analyzemath.com/trigonometry/sine.htm

(Click on the "click to start" button in the middle of the page")

edit: sorry, took ages searching my posts, so the above post wasn't there!

 

[Mona]

sinusoids 2

Maybe I should back up.

I understand how to get Function and the centerline and the amplitude.
I have a problem getting the period and the coeficient.

the graph is a line that flows from +10 on the y-axis to +2 -- on the downward slope (when the line is on 2) the interval is 3 PI -- when the line is on an upward slope (when it is on 10) the interval is 3 PI/2 --

The graph is a y=-cos x
the centerline is 6
amplitude 4

The period is 3 PI and I do not understand how they came to that conclusion.

 

[cristo]

I can't really picture the graph as you describe it. However, to get the period, you simply take the "length" of one complete cycle of the graph. Take the x value when the y value is (say) 0, and take the next x value when y=0. Then subtract the two, and you have the period.

 

[HallsofIvy]

Sine and cosine as functions (as opposed to when you are using them to solve parts of triangles) are defined so that the arguments (the "x" in sin(x)) have nothing to do with angles. Use "numbers" only as you correctly put it. However, the definitions of the sine and cosine functions are defined so that the "numbers" correspond to radians. (That's to keep engineers happy! They like to talk about "phase angles" when there are no angles concerned.)