Exploring the Tangent Graph in Trigonometry

The video tutorial introduces the graph of the tangent function using the unit circle. It explains how the tangent of an angle is derived from the sine and cosine values and visualizes this through the slope of a line. The tutorial explores specific angles like 0, pi/4, and -pi/4 to understand tangent values and their graphical representation. It discusses the behavior of the tangent function as it approaches vertical asymptotes at pi/2 and -pi/2, highlighting its periodic nature and how it repeats every pi radians.

What does the tangent of an angle represent in the context of a unit circle?

• The difference between the x and y coordinates of the point where the angle's ray intersects the unit circle.

• The product of the x and y coordinates of the point where the angle's ray intersects the unit circle.

• The ratio of the y-coordinate to the x-coordinate of the point where the angle's ray intersects the unit circle.

• The sum of the x and y coordinates of the point where the angle's ray intersects the unit circle.

What is the value of the tangent of theta when theta is 0 radians?

• 1

• Undefined

• 0

• -1

At what angle theta does the tangent of theta equal 1?

• pi/2 radians

• pi/4 radians

• pi radians

• 0 radians

What is the slope of the tangent function at theta equals negative pi over four radians?

• 1

• 0

• Undefined

• -1

What happens to the tangent of theta as theta approaches pi/2?

• It remains constant.

• It approaches infinity.

• It approaches 0.

• It approaches 1.

What characteristic does the graph of the tangent function show at pi/2 and -pi/2?

• Horizontal asymptotes

• Vertical asymptotes

• Intercepts at these points

• Remains constant

How does the graph of the tangent function behave as theta approaches negative pi over two?

• Approaches zero

• Approaches negative infinity

• Becomes undefined

• Approaches one

At what angle does the tangent function have a slope of negative one after crossing pi/2?

• 3 Pi/4 radians

• Pi radians

• 5 Pi/4 radians

• 2 Pi radians

What is the value of the tangent of theta at pi radians?

• 1

• -1

• 0

• Undefined

What is the period of the tangent function?

• 4 Pi radians

• Pi/2 radians

• 2 Pi radians

• Pi radians