Understanding the Tangent Function

This video tutorial covers the graphing of the tangent function using the unit circle. It explains the definition of the tangent function, both as a tangent segment and as the ratio of y/x. The video demonstrates how to graph the tangent function, highlighting its domain, range, and vertical asymptotes. It also provides a step-by-step guide on graphing the function by hand, emphasizing the function's period and lack of amplitude. The tutorial concludes with a summary of the tangent function's properties, including its symmetry and odd function nature.

What is the origin of the name 'tangent function'?

• It is derived from the tangent line that is parallel to the radius.

• It is derived from the tangent line that is perpendicular to the y-axis.

• It is derived from the tangent line that is perpendicular to the radius.

• It is derived from the tangent line that is parallel to the x-axis.

How can the value of tangent theta be defined?

• Using a tangent segment or the ratio Z/Y.

• Using a tangent segment or the ratio X/Z.

• Using a tangent segment or the ratio Y/X.

• Using a tangent segment or the ratio X/Y.

What happens to the tangent function as the angle approaches pi/2 radians?

• The function value approaches zero.

• The function value approaches negative infinity.

• The function value remains constant.

• The function value approaches infinity.

What is the significance of vertical asymptotes in the tangent function graph?

• They indicate where the function is zero.

• They indicate where the function is undefined.

• They indicate where the function is maximum.

• They indicate where the function is minimum.

What is the period of the tangent function?

• 2 pi radians

• pi radians

• 3 pi/2 radians

• pi/2 radians

How does the tangent function behave at negative angles?

• It is zero at negative angles.

• It behaves differently than positive angles.

• It behaves the same as positive angles.

• It is undefined at negative angles.

What is the domain of the tangent function?

• All real numbers except even multiples of pi/2.

• All real numbers except multiples of pi.

• All real numbers except odd multiples of pi/2.

• All real numbers except multiples of 2pi.

What is the range of the tangent function?

• All real numbers

• Only positive real numbers

• Only negative real numbers

• Only integers

What is the symmetry property of the tangent function?

• It is both even and odd.

• It is neither even nor odd.

• It is an odd function.

• It is an even function.

What is the amplitude of the tangent function?

• It has no amplitude.

• It has a minimum amplitude.

• It has a variable amplitude.

• It has a maximum amplitude.