Algebra 2: Sine and Cosine Functions

Which of the following have a frequency factor of b = 1? (Select all that apply)

When would two sine functions of the form y = sin(x - h) that have different values for h have the same graph?

Which of the following is the graph of y=cos(2(x+π))?

Which term gives the horizontal length of one cycle of a periodic function?

What is the period of y = sin(3x)?

Which term gives the number of cycles of a periodic function that occur in one horizontal unit?

Which transformations are needed to change the parent cosine function to y=0.35cos(8(x-π/4))?

The graph of y=sin(x-3π/2) is the graph of the y = sin(x) shifted in which direction?

What is the equation of the graph below?

Which of the following could be the equation of the function below?

What is the phase shift of a periodic function?

What is the general equation of a sine function with an amplitude of 2, a period of π, and a horizontal shift of π units?

Different sine functions ( y = \sin(x - h) ) can have the same graph if the ( h ) values differ by multiples of ( 2π ).
The period of ( y = \sin(3x) ) is ( \frac{2π}{3} ).

To transform the parent cosine function to ( y = 0.35\cos(8(x - \frac{π}{4})) ):
- Apply a vertical compression by a factor of 0.35.
- Apply a horizontal compression resulting in a period of ( \frac{π}{4} ).
- Implement a phase shift ( \frac{π}{4} ) units to the right.

The graph of ( y = \sin(x - \frac{3π}{2}) ) represents a shift of ( \frac{3π}{2} ) units to the right.
The equation of its cosine counterpart can be expressed as ( d: y = \cos(x + π) ).
An example function is given by ( y = -2\cos(2(x + π)) - 1 ).

Period: Defines the horizontal length of one cycle in periodic functions.
Phase Shift: Represents the horizontal translation of the function, altering its starting point along the x-axis.