Garrett C. answered • 08/31/21
Trigonometry Teacher of a Self-Designed Elective Course
What is the phase shift of y= -4sin 3(x-(pi/6) -7?
For basic trigonometric functions, the model of the function is as follows:
y = A * f(B(x +C)) + D
A = Amplitude of the Function
f(x) = Type of Function (sine, cosine, tangent, etc.)
B = Frequency of the Function (How many full waves occur in one standard period)
C = Phase Shift of the Function (left/right shift - sign is opposite of the standard direction)
D = Midline Equation/Vertical Shift of the Function (up/down shift - sign is the same as the direction)
The important thing to note is that the inside part of the function (following the trig. function) MUST BE FACTORED if applicable to be able to determine the phase shift. In the above function, it is, because the 3 is factored away from the x term. So in this case, the value associated with the "x" inside the parentheses is the phase shift (the - pi/6). As said before, the sign is OPPOSITE the standard direction - for a left/right shift, we would assume a "-" indicates going toward negative x, but it actually represents moving toward POSITIVE x. So the phase shift here for this function is RIGHT pi/6 units.
