What is the equation for a sine function with an amplitude of 4 and a period of $$\frac{\text{π}}{2}$$ ?

The equation is $$y = 4\text{sin}(4x)$$ .

What is the range of the sine function?

The range of the sine function is from -1 to 1, or in general, from $$d - |a|$$ to $$d + |a|$$ .

What is the relationship between sine and cosine functions?

Sine and cosine functions are phase-shifted versions of each other; specifically, $$\text{sin}(x) = \text{cos}(x - \frac{\text{π}}{2})$$ .

What is the period of the cosine function?

The period of the cosine function is also $$2\text{π}$$ .

How does changing the amplitude affect the sine function?

Changing the amplitude stretches or compresses the graph vertically; a larger amplitude results in taller peaks and deeper troughs.

What is the effect of changing the period on the sine function?

Changing the period affects the frequency of the wave; a shorter period results in more cycles in a given interval.

What is the equation for a cosine function with an amplitude of 5 and a period of $$\frac{\text{π}}{3}$$ ?

The equation is $$y = 5\text{cos}(6x)$$ .

What is the significance of the center line in a sine function?

The center line is the horizontal line that represents the average value of the function, around which the sine wave oscillates.

What is the maximum value of the sine function?

The maximum value of the sine function is equal to the amplitude, which is the coefficient $$a$$ in the equation $$y = a \text{sin}(bx)$$ .

A2 Period and Equations for Sin and Cos Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the period of the sine function?

Back

2.

FLASHCARD QUESTION

Front

What is the amplitude of a sine function?

Back

The amplitude of a sine function is the maximum distance from the center line to the peak or trough of the wave.

3.

FLASHCARD QUESTION

Front

How do you determine the period of a sine function given its equation?

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Where does the graph of sine begin?

Back

The graph of sine begins at the point (0, 0).

6.

FLASHCARD QUESTION

Front

What is the phase shift in a sine function?

Back

7.

FLASHCARD QUESTION

Front

What is the vertical shift in a sine function?

Back

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