How do you find the period of a transformed secant function $$y = a \text{sec}(bx - c) + d$$ ?

The period is calculated using the formula $$\frac{2\text{π}}{|b|}$$ .

What is the effect of the parameter 'b' in the function $$y = \text{sec}(bx)$$ ?

The parameter 'b' affects the horizontal stretch or compression of the graph.

What is the vertical asymptote of the secant function?

The vertical asymptotes occur where the cosine function is zero, i.e., at $$x = \frac{\text{π}}{2} + n\text{π}$$ for any integer n.

What is the vertical asymptote of the cosecant function?

The vertical asymptotes occur where the sine function is zero, i.e., at $$x = n\text{π}$$ for any integer n.

How do you graph the function $$y = \text{sec}(x)$$ ?

To graph $$y = \text{sec}(x)$$ , first graph $$y = \text{cos}(x)$$ , then draw vertical asymptotes where cos(x) = 0 and plot the secant values.

What is the relationship between secant and cosine functions?

The secant function is the reciprocal of the cosine function: $$\text{sec}(x) = \frac{1}{\text{cos}(x)}$$ .

What is the relationship between cosecant and sine functions?

The cosecant function is the reciprocal of the sine function: $$\text{csc}(x) = \frac{1}{\text{sin}(x)}$$ .

What is the transformation of the function $$y = \text{sec}(x) - 2$$ ?

This transformation shifts the graph of the secant function down by 2 units.

What is the transformation of the function $$y = 2\text{sec}(x)$$ ?

This transformation stretches the graph of the secant function vertically by a factor of 2.

Flashcardizz Graphs of Trigo Func (3B) Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of secant function (sec x)?

Back

2.

FLASHCARD QUESTION

Front

What is the definition of cosecant function (csc x)?

Back

3.

FLASHCARD QUESTION

Front

What is the period of the secant function?

Back

4.

FLASHCARD QUESTION

Front

What is the period of the cosecant function?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

The parameter 'a' affects the vertical stretch or compression of the graph.

7.

FLASHCARD QUESTION

Front

Back

The parameter 'd' translates the graph vertically by 'd' units.

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