How do you find the vertical asymptotes of $$y = \tan(4x)$$ ?

Set $$4x = \frac{\text{π}}{2} + n\text{π}$$ and solve for x.

What is the location of one vertical asymptote of $$y = \tan(4x)$$ ?

One vertical asymptote is at $$x = -\frac{\text{π}}{8}$$ .

What is the location of one vertical asymptote of $$y = \text{cot}(2(x - \frac{\text{π}}{4}))$$ ?

One vertical asymptote is at $$x = \frac{\text{π}}{4}$$ .

What is the relationship between tangent and cotangent functions?

Cotangent is the reciprocal of tangent: $$\text{cot}(x) = \frac{1}{\tan(x)}$$ .

What is the range of the tangent function?

The range of the tangent function is all real numbers, $$(-\text{∞}, \text{∞})$$ .

What is the range of the cotangent function?

The range of the cotangent function is all real numbers, $$(-\text{∞}, \text{∞})$$ .

What is the x-intercept of the tangent function?

The x-intercept occurs at $$x = n\text{π}$$ for integer n.

What is the x-intercept of the cotangent function?

The x-intercept occurs at $$x = \frac{n\text{π}}{2}$$ for odd integer n.

What is the effect of changing the coefficient in $$y = \tan(kx)$$ ?

Changing k affects the period: the new period is $$\frac{\text{π}}{k}$$ .

What is the effect of changing the coefficient in $$y = \text{cot}(kx)$$ ?

Changing k affects the period: the new period is $$\frac{\text{π}}{k}$$ .

Flashcard 2 (Trig Unit 2) - Tangent & Cotangent Flashcards

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1.

FLASHCARD QUESTION

Front

What is the period of the tangent function?

Back

2.

FLASHCARD QUESTION

Front

What is the period of the cotangent function?

Back

3.

FLASHCARD QUESTION

Front

What is the general form of the tangent function?

Back

4.

FLASHCARD QUESTION

Front

What is the general form of the cotangent function?

Back

5.

FLASHCARD QUESTION

Front

What are vertical asymptotes in the context of tangent and cotangent functions?

Back

6.

FLASHCARD QUESTION

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Back

7.

FLASHCARD QUESTION

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