Podcast
Questions and Answers
Which of the following have a frequency factor of b = 1? (Select all that apply)
Which of the following have a frequency factor of b = 1? (Select all that apply)
- A sine function whose graph shows 2 cycles from -4Ï€ radians to 0 (correct)
- A cosine function whose graph shows 1 cycle from 3Ï€ radians to 5Ï€ radians (correct)
- A cosine function with no phase shift whose x-coefficient is -1
- A sine function whose period is 2Ï€ radians (correct)
When would two sine functions of the form y = sin(x - h) that have different values for h have the same graph?
When would two sine functions of the form y = sin(x - h) that have different values for h have the same graph?
If the h-values differ by multiples of 2Ï€.
Which of the following is the graph of y=cos(2(x+Ï€))?
Which of the following is the graph of y=cos(2(x+Ï€))?
- Graph D
- Graph A
- Graph B (correct)
- Graph C
Which term gives the horizontal length of one cycle of a periodic function?
Which term gives the horizontal length of one cycle of a periodic function?
What is the period of y = sin(3x)?
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 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-Ï€/4))?
Which transformations are needed to change the parent cosine function to y=0.35cos(8(x-Ï€/4))?
The graph of y=sin(x-3Ï€/2) is the graph of the y = sin(x) shifted in which direction?
The graph of y=sin(x-3Ï€/2) is the graph of the y = sin(x) shifted in which direction?
What is the equation of the graph below?
What is the equation of the graph below?
Which of the following could be the equation of the function 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 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?
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?
Study Notes
Frequency and Period
- A sine function with a period of 2Ï€ has a frequency factor ( b = 1 ).
- The period of a function refers to the horizontal length of one complete cycle.
- The frequency indicates the number of cycles occurring in one horizontal unit.
Sine Function Characteristics
- Different sine functions ( y = \sin(x - h) ) can have the same graph if the ( h ) values differ by multiples of ( 2Ï€ ).
- The period of ( y = \sin(3x) ) is ( \frac{2Ï€}{3} ).
Transformations of Trigonometric Functions
- To transform the parent cosine function to ( y = 0.35\cos(8(x - \frac{Ï€}{4})) ):
- Apply a vertical compression by a factor of 0.35.
- Apply a horizontal compression resulting in a period of ( \frac{Ï€}{4} ).
- Implement a phase shift ( \frac{Ï€}{4} ) units to the right.
Graphs and Phase Shifts
- The graph of ( y = \sin(x - \frac{3Ï€}{2}) ) represents a shift of ( \frac{3Ï€}{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 ).
Key Terms
- 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.
Studying That Suits You
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Description
Test your knowledge on the changes in period and phase shift of sine and cosine functions with these flashcards. Understand the frequency factors and describe the behavior of the graphs through various scenarios. Perfect for reinforcing concepts in Algebra 2.
