What is the period of a transformed sine function?
The period of the sine function is 2π, which means that the value of the function is the same every 2π units.
What transformations affect the period of a sinusoidal function?
horizontal stretch (HS) alters the period. vertical stretch (VS) alters the amplitude. horizontal translation (HT) causes a phase shift relocating our initial point. vertical translation (VT) relocates the sinusoidal axis.
How does the period affect the graph of trigonometric functions?
Each period of the graph finishes at twice the speed. You can make the graph of a trig function move faster or slower with different constants: Positive values of period greater than 1 make the graph repeat itself more and more frequently. You see this rule in the example of f(x).
What affects a sine graph?
To conclude, when examining the graph y = a sin (bx + c), a affects the amplitude, b affects the period, and c affects the phase shift.
What happens to the frequency when the period of a sine function doubles?
When the period of a sine function doubles, the frequency 1 doubles.
What transformation affects the period?
The coefficient of x is the constant that determine the period. The general form is y = A sin Bx where |A| is the amplitude and B determines the period.
Does changing the period of a sine function change its domain?
Changing the period of a sine function changes its domain. T/F? Changing the vertical displacement of a cosecant function changes its range? You just studied 19 terms!
How do you find the period of a sine transformation?
For sine and cosine transformations, when A is larger than 1, the amplitude increases and is equal to the value of A; if A is negative, the graph reflects over the x-axis. When B is greater than 1, the period decreases; use the formula 2π/B to find the period.
What is the graph of the sine function?
The graph of the sine function is characterized by being a function that has a period of 2π. This means that the function repeats itself every 2π and extends indefinitely in both the positive and negative directions.
How do you find the period of a sin graph?
For sine and cosine transformations, when A is larger than 1, the amplitude increases and is equal to the value of A; if A is negative, the graph reflects over the x-axis. When B is greater than 1, the period decreases; use the formula 2π/B to find the period. How the values of A and B affect the shape of the graph y = A sin (Bx)?
What is the phase shift of sin x?
The phase shift is actually dependent on two parameters, b and c. Let’s go back to the fact that y = sin (x) cycles on 0 ≤ x ≤ 2π. Therefore, y = sin (bx + c) cycles on 0 ≤ bx + c ≤ 2π. Solving for x gives us –c/b ≤ x ≤ 2π/b – c/b.
