Precalculus 2/11/2010

Sinusoidal Graphs

y=Asin((x-C))+D

A= amplitude B= period C= phase shift D= sinusoidal axis

Remember to use Mr. Corn's 5 step process. It makes writing equations easier!

1. Sine or Cosine
2. Sinusoidal Axis
3. Amplitude
4. Phase Shift
5. Period

1. Cosine

It is possible to have different outcomes but I like to find a sine or cosine graph that starts at a specific point on the graph. I chose cosine because it is at pi.


2. +3
The green dotted line.

3. 2
The amplitude is from the sinusoidal axis to the top/bottom of the graph. The difference of 3 to 5 and 3 to 1 is 2.

4. -

The distance from the origin to my starting point. It is negative because you would subtract pi to get to the origin.



5.
11pi is where the graph repeats from the starting point. Subtracting pi from this, 10pi. REMEMBER this is your period, BUT you have to divide 2pi by 10pi to place it in the equation.

Now put everything together...


y=2cos((x-))+3


And again!





1. Cosine

Starting point- inbetween 4 and 2, which is 3.

2. +2

3. 6

4. -3

Starting point at 3, subtract 3 to get to the origin.

5.

The graph repeats at 13. Subtracting 3 from this you get a period of 10. Divde 2pi by 10 to get your 'formula ready' answer of pi over 5 (reduced).

Final:

y=6cos((x-3))+2

Have a fun LONG Weekend!

and

Don't forget Mr. Corn's Website here