Displacement of y=4+2sin(4+pi/2)

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Timothy

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Displacement of y=4+2sin(4x+pi/2). New Guy . This is the first time I have seen
an equation like this, with a number, like the four in front of the 2sin(4x+pi/2).
I know that the formula for displacement is-c/b, but I am not sure if this four
would change the equation. My book does not give any examples like this.


P.S. pi over the 2 is 3.14. I am not sure if this is the correct way to show this.

Need Help Thanks Tim[/b]
 
I am not sure of whay you need. perhaps someone else who does will also attempt to help.
example:
y = 4+ sin x is a sin wave that oscilates about the line y=4 and not y=0
The sin wave varies between 3 and 5 , and not between -1 and 1.
This is displaced upward by 4 units, as is your example

example
y=4+2 sin x is a sin wave displaced upward by 4 units,[it vibrates about the line y=4] and 2 sin x has a maximum of 2 and -2 .
Thus y= 4+ 2sinx varies between 2 and 6

example
y=sin4x has a period of 2pi/4, or the curve goes through a cyle in 2pi/4 , rather than 2pi

example
y=sin[x+@] is a sin wave shited left by @ In other words whae x=0 the y is not 0 but at the sin@.

I hope this helps
 
Timothy said:
I know that the formula for displacement is-c/b, but...
Click to expand...
Where do "c" and "b" come from? How do they relate to the trig function? What is your book's definition of "displacement"? For instance, does it refer to up/down shifting of the function, or left/right shifting? Or something else?

Please be specific. Thank you.

Eliz.
 
Displacement is the Phase Shift of a sine wave.

Example : For the sine function y=3sin (4x-2).

a=3 , b=4 , and c=-2

Displacement or (Phase Shift) = -c/b = - - 2/4 = 1/2

My orginal question was
Find the displacement of y = 4+ 2sin (4x+pi/2).

All I have to do is find the displacement of this function.
But I don't have any idea what to do with the first four and I am not
sure if it will effect the displacement.

My next class is Thursday . and I will ask my teacher.

Thanks Tim
 
y = 4 + 2sin(4x+pi/2)

a = 2, b = 4, c = pi/2, d = 4

horizontal displacement, or phase shift, = -c/b = -(pi/2)/4 = -pi/8 ... left pi/8 units.

another way to "see" the horizontal shift ...

y = 4 + 2sin[4(x + pi/8)]
 
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