What is the amplitude of a cosine function represented by the equation: $$y = \frac{1}{4}\text{cos}(3x + \frac{5\text{π}}{6}) - 7$$ ?

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

Identify the phase shift in the equation: $$f(x) = \text{cos}igg(\frac{x}{5} - \frac{\text{π}}{6}igg) + 2$$ .

The phase shift is $$\frac{5\text{π}}{6}$$ .

What does a phase shift of $$-\frac{\text{π}}{6}$$ indicate in a trigonometric function?

It indicates a shift to the left by $$\frac{\text{π}}{6}$$ units.

How do you determine the period of a sine function?

The period is calculated using the formula: Period = $$\frac{2\text{π}}{b}$$ , where b is the coefficient of x.

What is the effect of increasing the coefficient of x in a sine function?

Increasing the coefficient of x results in a shorter period.

What is the general form of a cosine function?

The general form is: $$y = A\text{cos}(Bx - C) + D$$ , where A is amplitude, B affects period, C is phase shift, and D is vertical shift.

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 does a negative amplitude indicate in a trigonometric function?

A negative amplitude reflects the graph across the midline.

How do you find the vertical shift of a trigonometric function?

The vertical shift is determined by the constant added or subtracted from the function.

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

The period is $$\frac{2\text{π}}{2} = \text{π}$$ .

What is the significance of the coefficient in front of the sine or cosine function?

The coefficient represents the amplitude of the wave.

SDC Pre-Cal 6.1-6.2 Qjiz Flashcards

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16 questions

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1.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

2.

FLASHCARD QUESTION

Front

Which function has an amplitude of 3?

Back

f(x) = 3 sin x.

Tags

CCSS.HSF.TF.A.4

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

4.

FLASHCARD QUESTION

Front

Back

The midline is y = -7.

Tags

CCSS.HSF-IF.C.7E

5.

FLASHCARD QUESTION

Front

Back

The amplitude is 2.

Tags

CCSS.HSF-IF.C.7E

6.

FLASHCARD QUESTION

Front

Define amplitude in the context of trigonometric functions.

Back

Amplitude is the maximum distance from the midline to the peak (or trough) of the wave.

Tags

CCSS.HSF-IF.C.7E

7.

FLASHCARD QUESTION

Front

What is the formula for finding the midline of a trigonometric function?

Back

The midline is found using the formula: Midline = Vertical Shift.

Tags

CCSS.HSF-IF.C.7E

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