I don't understand how to put the coordinates for sin and cos. All I know is that c/b is the phase shift.

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- January 25th 2010, 06:39 PMthisisamazingPhase Shift
I don't understand how to put the coordinates for sin and cos. All I know is that c/b is the phase shift.

- January 25th 2010, 07:50 PMProve It
- January 25th 2010, 08:52 PMthisisamazing
ok for example:

Sin(x+pi/2)

or

-1/2cos(4x+pi) - January 25th 2010, 11:40 PMGrandad
Hello thisisamazingFirst, try thinking about the value of that makes the expression in the brackets zero. This will tell you how far the 'basic' graph has been moved. So for example, in

(You'll see that I've put the word 'start' in quotes. That's because, of course, the graph doesn't actually start there; it extends infinitely far in each direction. But the cycle of the graph that we usually look at will start there.)

In the second example you give, :

However, a couple of other things have happened here as well:

- is multiplied by , which means that things happen times as fast along the -axis as they will on the 'basic' graph. So instead of requiring values of from to to make a complete cycle, you'll only need values from to .

- The cosine expression has then been multiplied by . This, in turn, does two things:

Does that help to make it clear?

- The minus sign flips the graph over, reflecting it in the -axis.

- The factor of reduces the -values to one-half of their original values, 'squashing' the graph down, so that, instead of varying between and , it will now vary between -0.5 and .

Grandad - is multiplied by , which means that things happen times as fast along the -axis as they will on the 'basic' graph. So instead of requiring values of from to to make a complete cycle, you'll only need values from to .
- January 26th 2010, 09:27 AMdavidman
I may not be OP, but Grandad, that was so easy to understand and super helpful for me.

I would like to double-check though. I recently found out about doubleangle formulae and different ways of writing

Would be the same as

and being 90 degrees,

- January 26th 2010, 10:34 AMGrandad