How can i find the phase shift of a trig graph? (cos/sin)

[abel muroi]

How can i find the phase shift of a trig graph? (cos/sin)

 

[Steven G]

How can i find the phase shift of a trig graph? (cos/sin)

1st you set the given angle to 0 and solve for x. Then you set the angle to 2pi and solve for x. Subtract the 2 x's (larger minus smaller).
EX: y=14 + 3sin(4x-5)
step 1: set 4x-5=0. Then 4x=5 then x=5/4
Step 2: set 4x-5=2pi. Then 4x=2pi+5. Then x=pi/2 + 5/4.
step 3: compute (pi/2 + 5/4) - (5/4) = pi/2

 

[abel muroi]

1st you set the given angle to 0 and solve for x. Then you set the angle to 2pi and solve for x. Subtract the 2 x's (larger minus smaller).
EX: y=14 + 3sin(4x-5)
step 1: set 4x-5=0. Then 4x=5 then x=5/4
Step 2: set 4x-5=2pi. Then 4x=2pi+5. Then x=pi/2 + 5/4.
step 3: compute (pi/2 + 5/4) - (5/4) = pi/2

i like your method but i think i found another method that might be easier..

do you think that this method will find any phase shift in a trig graph?...



y = a + b* cos/sin (c (x) + d)

y-intercept = a + b cos/sin (d)....................................... (((i removed c and x)))... (((y-intercept represents the point where the graph intersects the y-axis)))

y-intercept - a = b * cos/sin (d)........................................(((i subtracted a from both sides)))

y-intercept - a /b = cos/sin (d)....................................(((i divided both sides by b)))

after i do the algebra, i take the inverse of cos/sin and i get my phase shift

 

[Steven G]

i like your method but i think i found another method that might be easier..

do you think that this method will find any phase shift in a trig graph?...



y = a + b* cos/sin (c (x) + d)

y-intercept = a + b cos/sin (d)....................................... (((i removed c and x)))... (((y-intercept represents the point where the graph intersects the y-axis)))

y-intercept - a = b * cos/sin (d)........................................(((i subtracted a from both sides)))

y-intercept - a /b = cos/sin (d)....................................(((i divided both sides by b)))

after i do the algebra, i take the inverse of cos/sin and i get my phase shift

What??? Lets take the inverse. Then d=arcsin(-a/b). But you know d! and it probably does not equal arcsin(-a/b).
Why do you think that the value a would have anything to do with the phase shift, which is by the way a horizontal shift. The value a is a vertical shift. I gave you the steps. Now you decide if you want to use my method or your method.

 

[Steven G]

How can i find the phase shift of a trig graph? (cos/sin)

Abel, I am sorry but what I told you to do was the method to find the period. All you need to do to find the phase shift is just what I called step one. That is just set the angle equal to 0.
For example: y=3+5sin(2x-5)
2x-5=0 then 2x=5, then x=5/2