Trigonometric Functions and Their Properties

The video tutorial by Professor Dave covers the graphing of trigonometric functions, including sine, cosine, and tangent. It explains the domain and range of these functions, their periodic nature, and how to graph them using the unit circle. The tutorial also discusses transformations such as amplitude changes and phase shifts, and briefly covers the graphs of other trigonometric functions like cotangent, secant, and cosecant.

What is the range of the sine function?

• -∞ to ∞

• -1 to 1

• 0 to 2π

• All real numbers

Which trigonometric function has a range of all real numbers?

• Cosine

• Secant

• Tangent

• Sine

What is the period of the sine and cosine functions?

• 4π

• π/2

• π

• 2π

How does the graph of y = 2sin(x) differ from y = sin(x)?

• It has a period of π

• It is reflected across the x-axis

• It has an amplitude of 2

• It is shifted up by 2 units

What effect does a negative coefficient have on the graph of a sine function?

• It shifts the graph up

• It changes the period

• It increases the amplitude

• It reflects the graph across the x-axis

What is the period of the function y = sin(2x)?

• 4π

• π

• 2π

• π/2

In the function y = 4sin(2x - 2/3π), what is the phase shift?

• π/3 to the right

• 2/3π to the right

• 2/3π to the left

• π/3 to the left

What is the period of the tangent function?

• 2π

• π

• π/2

• 4π

How does the graph of cotangent differ from tangent?

• It has a period of 2π

• It is not periodic

• It rises to the right

• It falls to the right

What happens to the graph of cosecant at points where sine equals zero?

• It crosses the x-axis

• It has an asymptote

• It has a minimum

• It has a maximum