Trigonometric Functions and Their Properties

This video tutorial covers graphing trigonometric functions, including sine, cosine, secant, cosecant, tangent, and cotangent. It explains how to identify and graph these functions, focusing on amplitude, period, phase shifts, and vertical shifts. The tutorial also discusses the domain and range of these functions and provides examples of graphing variations with different parameters.

What is the main difference between the graphs of positive and negative sine functions?

• Positive sine starts at the bottom, negative sine starts at the top.

• Positive sine starts at the center and goes down, negative sine starts at the center and goes up.

• Positive sine starts at the center and goes up, negative sine starts at the center and goes down.

• Positive sine starts at the top, negative sine starts at the bottom.

How do you calculate the period of a sine or cosine wave?

• 2π divided by the number in front of X

• 2π divided by the amplitude

• 2π divided by the vertical shift

• 2π divided by the phase shift

What is the effect of a vertical shift on the graph of a sine function?

• It changes the amplitude of the graph.

• It shifts the graph up or down.

• It changes the period of the graph.

• It shifts the graph left or right.

How is the cosecant function related to the sine function?

• Cosecant is the inverse of sine.

• Cosecant is the reciprocal of cosine.

• Cosecant is the derivative of sine.

• Cosecant is the reciprocal of sine.

What is the domain of the cosecant function?

• All real numbers

• All real numbers except multiples of π

• All real numbers except odd multiples of π/2

• All real numbers except multiples of π/2

What is the period of the tangent function?

• π

• 2π

• 2π/3

• π/2

How does the graph of cotangent differ from that of tangent?

• Cotangent has a period of 2π, while tangent has a period of π.

• Cotangent is the reciprocal of tangent.

• Cotangent has vertical asymptotes at multiples of π, while tangent has them at multiples of π/2.

• Cotangent is an increasing function, while tangent is decreasing.

What happens to the graph of a tangent function when it is vertically stretched?

• The graph shifts upwards.

• The period of the graph increases.

• The graph becomes steeper.

• The graph becomes wider.

Which of the following is true about the range of the tangent function?

• It is all real numbers except multiples of π.

• It is limited to values between 0 and π.

• It is all real numbers.

• It is limited to values between -1 and 1.

What is the effect of a negative sign in front of a tangent function?

• It increases the period of the graph.

• It shifts the graph to the right.

• It decreases the amplitude of the graph.

• It reflects the graph over the x-axis.