precalc unit 5 sinusoids
what values (x/y) does D affect
y
what to remember with transformations
-a is a reflection over x AXIS
first output value for y=sin(angle) when 5 key points are plugged in
0 alternate up and down
cos functions have y int where
1
first output value for y=cos(angle)
1 alternate up and down
what can be the only outputs for parent sinusoid functions
1,0,-1
how to find c using a graph
cosine- how far do u have to go from Y axis to PEAK sin- how far do u have to go from y axis to NEXT POINT AT MIDLINE
how to find a using a graph
count up or down from the midline
sin starts _ and goes _
starts at MIDDLE and goes Up
cos starts at _ and goes _
starts at TOP and goes DOWN
how to make intervals (x axis)
take PERIOD and divide by 4 for ticks
what happens if a is negative
the amplitude is still positive there is just a reflection over x AXIS in transformations
what to pay attention to when writing the final equation modeling
the variable x t b
what is the difference between y=cos(angle) and y=sin(angle)
they are shifted from the same function
y axis intervals
up 4 lines is 1 down 4 lines is -1
what to pay attention to when graphing from given points
when going up or down, make sure the scale factor (A) is applied to it reflections when sin DOESNT GO UP how these reflections affect the D
5 key points for sin and cos
wuadrantals
what values (x/y) does B affect
x
what values (x/y) does C affect
x
what values (x/y) does A affect
y
what to remember when writing equations for graphs
y= c= transformation from original to get to new one in graph, not what you need to do to get the graphed one to the original
x values are always
0 pi/2 pi 3pi/2 2pi
what are the 5 key X values
0 pi/2 pi 3pi/2 2pi
how to determine the midline
Y=D
how to determine the frequency of a sinusoid
1/T inverse of period
how long is the period of sine and cosine
2pi
how to find b using a graph
2pi/ period
how to determine the period of a sinusoid
2pi/absolute value of B
how to find how to find B value when modeling
2pi/period
A= f= T=
A=amplitude f=frequency (1/T) T= period (2pi/B)
y=sinA(B(x-C))+D A= B= C= D=
A=vertical stretch/shrink =reflect over x axis B=horizontal shrink/stretch =reflect over y axis C= shift left or right D= shift up or down
what is the amplitude if a sinusoid
ABSOLUTE VALUE of A will always be positive
what represents the horizontal/phase shift
C
what letter represents vertical shift
D
phase shift and horizontal stretch/shrink are
OPPOSITE WHAT YOU THINK
what to remember with any kind of stretch
SCALE BIGGER THAN 1 pi=3.14, make sure it's in the correct spot
letter to represent period
T=
what to remember when writing the period in modeling
T=
what does it mean to be a periodic
a function that repeats the same pattern over and over
how to determine heights
amplitude (a)
where should the middle be
at the midline
how to determine the output of the quadrantals (inputs) when the question asks for SIN
plug in the Y values of the unit circle plug in first go all the way up, then all the way back down
how to graph when given points and A B
determine A Determine B determine the transformations to get to sin and cosine (from original TO NEW) (up down, left right)
how to graph a sinusoid
determine all parts determine transformations find key points make intervals graph make sure it doesn't go above or below values do more than one period
how to find phase shift
determine how far right or left u go depending on if ur given a sin or cos equation to write
x axis intervals
every 2 pi/2 pi 3pi/4 2pi
how to write a sinusoid
find ABCD write y=
how to make intervals (y axis)
go as high/ low as new y values do
how to determine y axis intervals
graph midline determine amplitude go up and down from midline
what to pay attention to when graphing
how many periods it is asking for asking for 2- need 2 peaks and drops
what to remember to do with a function
if there is a coefficient infront of the x, factor it out to make it the b value
how to find vertical shift d in modeling
max y+ min y/ period average max and min OVER PERIOD, NOT 2 LIKE IN AMPLITUDE
how to find amplitude when modeling
max y-min y/2 MINUS NOT PLUS LIKE IN VERTICAK SHIFT
how to find d using graph
midline
how does A impact the 5 key points of the parent function
multiply the y coordinates by a (vertical stretch or shrink by_)
what does the numerator and denominator of the frequency mean
numerator= # of cycles denominator= per _ units
what is a period
one wavelength the width of one complete cycle
sin functions have y intercept where
origin
how to determine width
period (b)
what functions are sinusoids
sin and cosine
