Trigonometric Functions and Their Properties

The video tutorial explains the relationship between cosine and sine, highlighting how the cosine graph is a horizontally shifted version of the sine graph. It then delves into the properties of the tangent graph, focusing on asymptotes and the behavior of the graph as the denominator approaches zero. The tutorial concludes with a discussion on the periodicity of trigonometric functions, emphasizing how the combination of sine and cosine results in a periodic function with a period of 180 degrees.

What is the primary difference between the sine and cosine graphs?

• Cosine graph is a vertically shifted version of sine graph.

• Cosine graph is a horizontally shifted version of sine graph by 90 degrees.

• Cosine graph is a reflection of sine graph over the x-axis.

• Cosine graph is a reflection of sine graph over the y-axis.

What happens to the tangent graph at the points where cosine equals zero?

• The tangent graph has a peak.

• The tangent graph crosses the x-axis.

• The tangent graph has a vertical asymptote.

• The tangent graph has a trough.

How does the tangent graph behave as it approaches an asymptote?

• It remains constant.

• It oscillates between two values.

• It approaches infinity or negative infinity.

• It flattens out.

What happens to the tangent graph when the numerator is zero?

• The graph reaches a minimum point.

• The graph reaches a maximum point.

• The graph crosses the x-axis.

• The graph has a vertical asymptote.

What is the period of the sine and cosine functions?

• 270 degrees

• 360 degrees

• 180 degrees

• 90 degrees

What is the period of the tangent function?

• 90 degrees

• 180 degrees

• 360 degrees

• 270 degrees

What is the relationship between the periods of sine, cosine, and tangent functions?

• Tangent has a longer period than sine and cosine.

• All three have the same period.

• Sine and cosine have the same period, tangent has a different one.

• Sine has a longer period than cosine and tangent.

How does the tangent graph differ from the cubic graph at the origin?

• Tangent graph has a non-zero gradient at the origin.

• Tangent graph has a vertical tangent at the origin.

• Tangent graph has no gradient at the origin.

• Tangent graph has a horizontal tangent at the origin.

What is the range of the tangent function?

• Between -1 and 1

• All real numbers

• Only positive numbers

• Only negative numbers

Why does the tangent graph have holes?

• Because the graph is periodic.

• Because tangent is undefined at those points.

• Because cosine is zero at those points.

• Because sine is zero at those points.