Understanding the Tangent Function

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.

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)

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

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

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

What are the vertical asymptotes of the tangent function?

• x = n*pi/2

• x = pi/2 + n*pi

• x = 2n*pi

• x = n*pi

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

What is the range of the tangent function?

• Only positive real numbers

• Only negative real numbers

• All real numbers

• Only integers

What does the tangent function represent in terms of a circle?

• The radius of the circle

• The diameter of the circle

• The slope of the terminal side of an angle

• The circumference of the circle

Which of the following is a key concept related to the tangent function?

• Tangent has vertical asymptotes

• Tangent is undefined at integer multiples of pi

• Tangent is always positive

• Tangent has no zeros

What is the relationship between the zeros of tangent and its x-intercepts?

• Zeros are the same as x-intercepts

• Zeros occur at y-intercepts

• They are unrelated

• Zeros are the opposite of x-intercepts