Trigonometric Functions and Their Properties

The video tutorial by Professor Dave covers graphing trigonometric functions, focusing on 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 covers transformations such as amplitude changes and phase shifts, and briefly discusses graphing other trigonometric functions like cotangent, secant, and cosecant.

What is the range of the sine function?

• All real numbers

• 0 to 2π

• -1 to 1

• -∞ to ∞

Which trigonometric function has a range of all real numbers?

• Secant

• Cosine

• Tangent

• Sine

What is the period of the sine and cosine functions?

• 2π

• 4π

• π

• π/2

At what angle does the sine function first reach its maximum value?

• 0

• π/2

• 3π/2

• π

How does a negative coefficient affect the graph of a sine function?

• It shifts the graph horizontally.

• It stretches the graph vertically.

• It compresses the graph horizontally.

• It reflects the graph across the x-axis.

What is the amplitude of the function y = 3sin(x)?

• 1

• 2

• 3

• 4

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

• π/2

• 2π

• 4π

• π

Which trigonometric function has vertical asymptotes?

• Sine

• Cosine

• Cosecant

• Tangent

How does the graph of cotangent differ from tangent?

• It rises to the right instead of falling.

• It has a different period.

• It is shifted horizontally.

• It has no asymptotes.

What happens to the graph of secant at points where cosine is zero?

• It reaches a minimum.

• It crosses the x-axis.

• It has a vertical asymptote.

• It reaches a maximum.