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# Create Trigonometric Models

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1.  2.  3.  4.  I have 1 and 2 graphs up there just to show how they are graphing it

Jan 23, 2018

#1
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1.   y  =  3sin [  (1/2) x ]  -  5

This is the normal sine function with an amplitude of 3.....shifted down 5 units   ....and with a period twice as long as the normal function

A max y value will be   when x  =  pi  =  3.14  ....so y  = -2

And a  min  y value  occurs  at x =   3 pi  =  9.42.....so y will be =  - 8

So the midline will be at  y  =  [ -2 - 8 ] / 2  =  -10/2  =  -5

The  first  point  will be   at  ( 0, - 5)

The second point [going from left to right ] will be a max  and will occur at  (pi, -2)  =   (3.14, -2)

Here's the graph  : https://www.desmos.com/calculator/jeq6vpldcz   Jan 23, 2018
edited by CPhill  Jan 23, 2018
#2
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2.    y    =  3cos(2x) - 1

This is the normal cosine graph with a period of pi (3.14)....an amplitude of 3...and shifted down 1 unit

A max occurs at  (0, 2)

A min occurs  at  ( pi/2, - 4)  =  (1.57, -4)

So.....the midline  is  (2 - 4)  / 2  =  -2/ 1  =   -1

So...the first point will occur at   (pi/4, -1)  = (.785, -1)

And the next point [ going from  left to right ] is a min   and will occur at  ( pi/2, -4)  =  (1.57, -4)

Here's a graph  : https://www.desmos.com/calculator/o492neu3zh   Jan 23, 2018
#3
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3.  The first answer is correct

See the graph here : https://www.desmos.com/calculator/svuut8vshm   Jan 23, 2018