Can anyone remember the formulas of period, phase shift and range of the sin function?

This is an old post that was our "reference material" sticky note topic.

It is worth looking at!

http://web2.0calc.com/questions/graphing-trig-functions_1#rr2

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Ninja, could you please reference this whole thread underneath it - thank you.  Melody.

$$Do you mean$$ A*sin(\frac{2\pi t}{T}+\phi) $$\\ where A is maximum amplitude, t is time, T is period and $\phi$ is phase angle? The range is then $\pm A$$ $

y=A*sin(B*x-C)+D

How do A,B,C and D change the sin function. What formulas I can use to find out Amplitude, Period, Phase Shift and Range? Do I have to create the graph? Also if you know a link to share with me that shows changes I would apreciate it.

Here's a pretty good page that explains it all.......(I can't add anything, so I won't !!!)

http://www.intmath.com/trigonometric-graphs/trigo-graph-intro.php

Thanks I will check that page.

y=A*sin(B*x-C)+D

Here, B is 2pi/L where L is the (presumably spatial) period.  As L gets bigger the sine wave "stretches out"; as it gets smaller, the wave oscillates more rapidly.

-C is the phase shift.  When C is zero the sin wave starts at zero (and y starts at D) when x is zero.

A is the maximum amplitude.  As A gets bigger the peak to trough variation gets bigger.

D is a fixed offset.  It's the average value about which the sin wave oscillates.