How do you determine the amplitude from the function $$f(x) = a \, \text{cos}(bx + c) + d$$ ?

The amplitude is the absolute value of $$a$$ . It represents the maximum height of the wave from its midline.

What is the phase shift in the function $$f(x) = a \, \text{cos}(bx + c) + d$$ ?

The phase shift is given by $$-\frac{c}{b}$$ . It indicates how much the graph is shifted horizontally from the origin.

Identify the amplitude in the equation: $$y = \frac{1}{4} \, \text{cos}(3x + \frac{5\theta}{6}) - 7$$ .

The amplitude is $$\frac{1}{4}$$ .

What does the value of $$b$$ represent in the function $$f(x) = a \, \text{cos}(bx + c) + d$$ ?

The value of $$b$$ affects the period of the function. The period is calculated as $$\frac{2\theta}{b}$$ .

What is the period of the function $$f(x) = 3 \, \text{sin}(2x)$$ ?

The period is $$\frac{2\theta}{2} = \theta$$ .

How do you find the vertical shift in the function $$f(x) = a \, \text{cos}(bx + c) + d$$ ?

The vertical shift is represented by $$d$$ , which moves the graph up or down on the y-axis.

What is the difference between sine and cosine functions?

Sine functions start at the midline and go up, while cosine functions start at the maximum value. Their graphs are phase-shifted by $$\frac{\theta}{2}$$ .

What is the maximum value of the function $$f(x) = 2 \, \text{sin}(x) - 3$$ ?

The maximum value is $$2 - 3 = -1$$ .

What is the minimum value of the function $$f(x) = 2 \, \text{cos}(x) + 1$$ ?

The minimum value is $$-2 + 1 = -1$$ .

How do you identify the values of $$a$$ , $$b$$ , and $$c$$ in the function $$f(x) = a \, \text{cos}(bx) + c$$ ?

$$a$$ is the amplitude, $$b$$ affects the period, and $$c$$ is the vertical shift.

What is the effect of changing the value of $$a$$ in the function $$f(x) = a \, \text{sin}(x)$$ ?

Changing the value of $$a$$ alters the amplitude of the sine wave, making it taller or shorter.

What is the significance of the graph of a trigonometric function?

The graph visually represents the behavior of the function, showing its amplitude, period, phase shift, and vertical shift.

SDC Pre-Cal 6.1-6.2 Qjiz Flashcards

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1.

FLASHCARD QUESTION

Front

What is the amplitude of a function?

Back

The amplitude of a function is the maximum distance from the midline of the graph to its peak or trough. It is a measure of how far the graph rises or falls from its central value.

Tags

CCSS.HSF-IF.C.7E

2.

FLASHCARD QUESTION

Front

Define the term 'period' in trigonometric functions.

Back

Tags

CCSS.HSF.TF.A.4

3.

FLASHCARD QUESTION

Front

What is the general form of a cosine function?

Back

Tags

CCSS.HSF-IF.C.7E

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

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