What type of trigonometric function is used to model periodic behavior?

Sine and cosine functions are commonly used to model periodic behavior.

What is the general form of a cosine function?

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

What is the relationship between the string length and the amplitude in a yo-yo model?

The amplitude is half the length of the string if the yo-yo swings from the highest to the lowest point.

What is the significance of the horizontal shift in a trigonometric function?

The horizontal shift determines where the function starts on the x-axis.

How can you identify if a function is modeled by a sine or cosine function?

If the function starts at its maximum or minimum, it is likely a cosine function; if it starts at the midline, it is likely a sine function.

What is the period of a sine function with an angular frequency of $$b = \frac{2\theta}{p}$$ ?

The period is given by $$p = \frac{2\theta}{b}$$ .

What is the effect of changing the value of b in a trigonometric function?

Changing the value of b affects the period of the function; a larger b results in a shorter period.

How do you find the midline of a trigonometric function?

The midline is found by averaging the maximum and minimum values of the function.

Modeling w/Trig Functions Homework Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the formula to find the period (p) of a trigonometric function?

Back

2.

FLASHCARD QUESTION

Front

How do you calculate the angular frequency (b) from the period (p)?

Back

3.

FLASHCARD QUESTION

Front

What is the vertical shift in a trigonometric function?

Back

The vertical shift is the midpoint between the maximum and minimum values of the function.

4.

FLASHCARD QUESTION

Front

How do you determine the amplitude of a trigonometric function?

Back

The amplitude is the distance from the midline (vertical shift) to the maximum or minimum value.

5.

FLASHCARD QUESTION

Front

Back

The amplitude is 2.

6.

FLASHCARD QUESTION

Front

Back

The maximum value is 7 (5 + 2).

7.

FLASHCARD QUESTION

Front

Back

The minimum value is 3 (5 - 2).

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