Understanding the Tangent Function

Understanding the Tangent Function

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Patricia Brown

FREE Resource

The video tutorial explores the tangent function, starting with its identity as sine over cosine. It explains how to find the zeros of the tangent function, which correspond to the x-intercepts on its graph. The tutorial also covers the concept of vertical asymptotes, where the tangent function is undefined, and discusses the domain and range of the tangent function, highlighting that the range includes all real numbers.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the identity of the tangent function in terms of sine and cosine?

tangent theta = cosine theta / sine theta

tangent theta = sine theta / cosine theta

tangent theta = sine theta * cosine theta

tangent theta = 1 / (sine theta * cosine theta)

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

At which points does the tangent function have zeros?

At integer multiples of pi

At odd multiples of pi/2

At even multiples of pi/2

At integer multiples of pi/4

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How are the zeros of the tangent function related to its graph?

They are the y-intercepts

They are the points of inflection

They are the x-intercepts

They are the vertical asymptotes

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When is the tangent function undefined?

When theta equals zero

When sine theta equals zero

When cosine theta equals zero

When both sine and cosine are zero

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the vertical asymptotes of the tangent function?

x = n*pi/2

x = pi/2 + n*pi

x = 2n*pi

x = n*pi

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is true about the domain of the tangent function?

All real numbers

Only integer multiples of pi

All real numbers except integer multiples of pi

All real numbers except odd multiples of pi/2

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the range of the tangent function?

Only positive real numbers

Only negative real numbers

All real numbers

Only integers

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