Write a sine equation for period= pie, amplitude=1/2, vertical shift up 1 and phase shift left pie/4. How would the equation be written?
What do you think? I will be happy to check your work.
Y= 1/2 sin pi (x+pi/4) -1
remember that the period of sin kx is 2π/k
so your function will have to be of the form
y = sin 2x
inserting the other stuff , you would have
y = (1/2) sin 2(x + π/4) + 1
Check with your answer
To write the sine equation with the given specifications, you can start with the general form of a sine function:
y = A*sin(B(x - C)) + D
Where:
A represents the amplitude.
B determines the period of the function.
C is the phase shift.
D is the vertical shift or the midline.
In this case, the given specifications are:
Period = π
Amplitude = 1/2
Vertical shift = 1 (up)
Phase shift = π/4 (left)
Let's plug the values into the general form:
A = 1/2
B = 2π/Period = 2π/π = 2
C = -phase shift = -π/4
D = vertical shift = 1
Substituting the values, we get:
y = (1/2)*sin(2(x - (-π/4))) + 1
Simplifying further:
y = (1/2)*sin(2(x + π/4)) + 1
Therefore, the equation for the sine function with a period of π, amplitude of 1/2, vertical shift up 1, and phase shift left π/4 would be:
y = (1/2)*sin(2(x + π/4)) + 1