Write the equation of a sine function with amplitude 2, period $$\frac{2\text{π}}{3}$$ , and vertical shift of 1.

The equation is $$y = 2\text{sin}(3x) + 1$$ .

How do you find the low point of a sinusoidal function?

The low point can be found using $$\text{Low Point} = \text{Vertical Shift} - \text{Amplitude}$$ .

What is the relationship between sine and cosine functions?

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

How do you calculate the height of a point on a sinusoidal function?

To calculate the height, substitute the x-value into the function $$y = a \text{sin}(bx - h) + k$$ or $$y = a \text{cos}(bx - h) + k$$ .

What is the significance of the coefficient 'b' in a sinusoidal function?

The coefficient 'b' affects the frequency and period of the function. A larger value of b results in a shorter period.

Define the term 'frequency' in relation to sinusoidal functions.

Frequency is the number of cycles a sinusoidal function completes in a unit interval, calculated as $$\text{Frequency} = \frac{1}{\text{Period}}$$ .

What is the equation of a cosine function with amplitude 4, period $$2\text{π}$$ , phase shift of $$\frac{\text{π}}{3}$$ , and vertical shift of 2?

The equation is $$y = 4\text{cos}(x - \frac{\text{π}}{3}) + 2$$ .

How do you determine the x-intercepts of a sinusoidal function?

To find the x-intercepts, set the function equal to zero and solve for x.

What is the effect of a negative amplitude in a sinusoidal function?

A negative amplitude reflects the graph across the midline, effectively flipping it vertically.

Unit 4B: Sinusoidal Practice Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean identity for sine and cosine?

Back

Tags

CCSS.HSF.TF.C.8

2.

FLASHCARD QUESTION

Front

Define amplitude in the context of sinusoidal functions.

Back

Tags

CCSS.HSF-IF.C.7E

3.

FLASHCARD QUESTION

Front

What is the formula for the period of a sinusoidal function?

Back

Tags

CCSS.HSF.TF.A.4

4.

FLASHCARD QUESTION

Front

How do you determine the vertical shift of a sinusoidal function?

Back

Tags

CCSS.HSF-IF.C.7E

5.

FLASHCARD QUESTION

Front

What is the maximum height of a sinusoidal function given its amplitude and vertical shift?

Back

Tags

CCSS.HSF.TF.A.4

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

7.

FLASHCARD QUESTION

Front

What does the phase shift represent in a sinusoidal function?

Back

Tags

CCSS.HSF-IF.C.7E

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