Identify the amplitude, period, phase shift and vertical shift when appropriate.
1. y=sin(x+pi/2)
2. y=sin (x -pi) – 2
3. y=1/2cos(2x)
4. y=2sin(2x+pi)-3
Nemo = Jackson
Why are you switching names? Didn't you understand what bobpursley posted for you earlier?
Y=Amplitide* sinorCos (x+phaseShift) + vertical shift is standard form.
i changed names because im afraid to ask again. im so confused on this class and my teacher doesnt have time to help me and they are different problems. i dont know how to do anything for math because all that is given is the assignments and then we are on our own to figure it out. im sorry i just need to get all ten assignments done before friday and now im just desperate. i was afraid someone was going to get mad at me.
all you need to work these is to recall that
sin(ax) has period 2π/a
sin(x-b) has a phase shift of b to the right.
so, sin(ax-b) = sin(a(x - b/a)) has period 2π/a and a phase shift of b/a
y = f(x)+k has a vertical shift of +k
So,
1. y=sin(x+pi/2)
amplitude: 1
period: 2pi
phase shift: -pi/2
vertical shift: 0
2. y=sin (x -pi) – 2
amplitude: 1
period: 2pi
phase shift: pi
vertical shift: -2
3. y=1/2cos(2x)
amplitude: 1/2
period: 2pi/2 = pi
phase shift: 0
vertical shift: 0
4. y=2sin(2x+pi)-3
amplitude: 2
period: pi
phase shift: -pi/2
vertical shift: -3
No one will get mad. Just pick one name and keep it. Then you'll be able to find your other posts just by clicking on your name. In addition, the tutors will be able to help you better if they can see what you have asked before and where you run into trouble.
In addition to bob's and oobleck's replies, be sure to make good use of https://www.khanacademy.org/ -- just scroll down until you find the type of math (or any other subject) you need help with.
To identify the amplitude, period, phase shift, and vertical shift, we need to understand the general form of trigonometric equations.
1. y = sin(x + π/2):
- Amplitude: The amplitude of a function is the absolute value of the coefficient of the trigonometric function. In this case, the amplitude is 1.
- Period: The period of a function is given by 2π divided by the coefficient of x inside the trigonometric function. Here, the period is 2π.
- Phase Shift: The phase shift occurs when there is a constant term added or subtracted inside the trigonometric function. In this case, there is a phase shift of -π/2 (to the right) since x is replaced by (x + π/2).
- Vertical Shift: There is no vertical shift in this case.
2. y = sin(x - π) - 2:
- Amplitude: The amplitude remains 1.
- Period: The period remains 2π.
- Phase Shift: There is a phase shift of π (to the right) since x is replaced by (x - π).
- Vertical Shift: The function is shifted downward by 2 units.
3. y = (1/2)cos(2x):
- Amplitude: The amplitude is given by the absolute value of the coefficient in front of the trigonometric function, which is 1/2.
- Period: The period is found by dividing 2π by the coefficient of x inside the trigonometric function. In this case, it is π.
- Phase Shift: There is no phase shift in this case since there is no constant term added or subtracted inside the trigonometric function.
- Vertical Shift: There is no vertical shift.
4. y = 2sin(2x + π) - 3:
- Amplitude: The amplitude is given by the absolute value of the coefficient in front of the trigonometric function, which is 2.
- Period: The period is found by dividing 2π by the coefficient of x inside the trigonometric function. Here, it is π.
- Phase Shift: There is a phase shift of -π/2 (to the right) since x is replaced by (2x + π).
- Vertical Shift: The function is shifted downward by 3 units.
By analyzing the given trigonometric equations, we can determine the amplitude, period, phase shift, and vertical shift for each of them.