What is the phase shift of the function $$y=\text{cos}(x-\frac{\text{π}}{2})$$ ?

The phase shift is $$\frac{\text{π}}{2}$$ to the right.

What is the period of a sine function given by $$y=a\text{sin}(bx)$$ ?

The period is calculated as $$\frac{2\text{π}}{|b|}$$ .

What is the amplitude of a trigonometric function?

The amplitude is the maximum distance from the midline to the peak (or trough) of the graph, determined by the absolute value of a in the equation $$y=a\text{sin}(b(x-h))+k$$ .

How do you determine the direction of a horizontal shift in a trigonometric function?

The direction of the horizontal shift is determined by the sign of h in the function $$y=a\text{sin}(b(x-h))+k$$ ; if h is positive, the shift is to the right, and if h is negative, the shift is to the left.

What is the effect of changing the value of b in the function $$y=a\text{sin}(bx)$$ ?

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

What is the general form of a transformed sine function?

The general form is $$y=a\text{sin}(b(x-h))+k$$ , where a is the amplitude, b affects the period, h is the phase shift, and k is the vertical shift.

What is the general form of a transformed cosine function?

The general form is $$y=a\text{cos}(b(x-h))+k$$ , where a is the amplitude, b affects the period, h is the phase shift, and k is the vertical shift.

How do you graph a transformed trigonometric function?

To graph a transformed trigonometric function, identify the amplitude, period, phase shift, and vertical shift, then plot key points and sketch the curve accordingly.

What is the relationship between sine and cosine functions?

Sine and cosine functions are related by a phase shift of $$\frac{\text{π}}{2}$$ ; specifically, $$\text{sin}(x) = \text{cos}(x - \frac{\text{π}}{2})$$ .

Transformations of Trigonometric Functions HW Flashcards

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16 questions

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1.

FLASHCARD QUESTION

Front

What is the midline in a trigonometric function?

Back

2.

FLASHCARD QUESTION

Front

Back

The parameter k affects the midline.

3.

FLASHCARD QUESTION

Front

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

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What does the vertical shift in a trigonometric function indicate?

Back

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