Effects of Amplitude on Tan Graph

This video tutorial explores the amplitude of the tangent graph, focusing on how the 'a' parameter affects the steepness of the graph. It compares different cases: y = tan x, y = 2 tan x, y = -tan x, and y = 0.5 tan x, highlighting how changes in the 'a' value impact the graph's steepness. The video emphasizes that unlike other trigonometric graphs, the tangent graph does not have a minimum or maximum, so attention must be paid to the slope. Viewers are encouraged to watch additional videos for more information on other parameters of the tangent graph.

What is the main focus of the video regarding the tan graph?

• Phase shift and its effects

• Frequency and its effects

• Amplitude and its effects

• Vertical shift and its effects

How does a positive amplitude, such as in y = 2 tan x, affect the tan graph?

• It makes the graph flatter

• It makes the graph steeper

• It shifts the graph horizontally

• It shifts the graph vertically

What happens to the tan graph when the amplitude is negative, as in y = -tan x?

• The graph shifts upwards

• The graph shifts to the right

• The graph reflects over the x-axis

• The graph becomes steeper

In the case of y = 0.5 tan x, how does the fractional amplitude affect the graph?

• The graph reflects over the y-axis

• The graph becomes flatter

• The graph becomes steeper

• The graph shifts downwards

What is the effect of a smaller amplitude on the tan graph?

• It shifts the graph upwards

• It makes the graph steeper

• It makes the graph flatter

• It shifts the graph to the left

Why is it important to pay attention to the slope of the tan graph?

• Because it determines the graph's frequency

• Because it affects the graph's vertical shift

• Because it shows changes in amplitude

• Because it indicates the graph's phase shift

What is unique about the tan graph compared to the cosine graph?

• It does not have a minimum or maximum

• It has a minimum and maximum

• It has a constant frequency

• It has a constant amplitude

How does a larger amplitude affect the tan graph?

• It shifts the graph downwards

• It makes the graph steeper

• It makes the graph flatter

• It shifts the graph to the left

What is the value of the tan graph at 45 degrees for y = tan x?

• 0

• 1

• -1

• 2

What is the value of the tan graph at 45 degrees for y = 0.5 tan x?

• 0

• 2

• 0.5

• 1