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Graphing Sine and Cosine Flashcards

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Questions and Answers

What is the maximum of f(x) = sin(x)?

Which function is graphed below?

f(x) = tan(x)

f(x) = sin(x)

f(x) = cos(x) (correct)

f(x) = sec(x)

The graph of which function passes through (0,4) and has a minimum value?

Which set of transformations is needed to graph f(x) = -2sin(x) + 3 from the parent sine function?

Reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up Signup and view all the answers

Which function describes the graph shown below?

A Signup and view all the answers

Which function describes the graph below?

B Signup and view all the answers

Which function has the given properties below? The domain is the set of all real numbers. One x-intercept is provided. The amplitude is 4. The point is on the graph. The y-intercept is (0, 0).

y = -4sin(x) Signup and view all the answers

Which function has the given properties below? The domain is the set of all real numbers. One x-intercept is provided. The maximum value is 3. The y-intercept is (0, -3).

y = -3cos(x) Signup and view all the answers

What is the domain of f(x) = cos(x)?

the set of all real numbers Signup and view all the answers

What is the amplitude of the function below?

2 Signup and view all the answers

Study Notes

Maximum and Minimum Values

The maximum value of the sine function, f(x) = sin(x), is 1.
A function can have a specific minimum value based on its transformations and inherent characteristics.

Function Identification

The function graphed below corresponds to f(x) = cos(x).
When identifying functions from their graphs, key points and symmetry help determine their nature.

Transformations of Sine Functions

For the function f(x) = -2sin(x) + 3, transformations include:
- Reflection across the x-axis
- Vertical stretching by a factor of 2
- Vertical translation upward by 3 units

Properties of Functions

A function described by certain properties must have characteristics such as domain, amplitude, x-intercepts, and y-intercepts.
For example, y = -4sin(x) has a domain of all real numbers, an amplitude of 4, and passes through specific points.

Domain of Cosine Function

The domain of the cosine function, f(x) = cos(x), includes all real numbers, indicating it is defined for every x value.

Amplitude

The amplitude of a sine or cosine graph reflects the distance from its midline to its maximum or minimum value; for the specified function, the amplitude is 2.

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Description

Test your knowledge on graphing sine and cosine functions with these flashcards. Each card presents a different scenario or question related to sine and cosine graphs, including transformations and properties. Perfect for those studying trigonometry.