Trigonometric Functions and Their Properties

The video tutorial by Professor Dave covers the graphing of 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 discusses transformations such as amplitude changes, period adjustments, and phase shifts. Additionally, it provides an overview of other trigonometric functions like cotangent, secant, and cosecant, highlighting their unique graph characteristics.

What is the range of the sine function?

• -1 to 1

• -∞ to ∞

• 0 to 2π

• All real numbers

Which trigonometric function has a range of all real numbers?

• Sine

• Cosine

• Secant

• Tangent

What is the period of the sine function?

• π

• 2π

• π/2

• 4π

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

• It is reflected over the x-axis

• It has a smaller period

• It has a larger amplitude

• It is shifted to the right

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

• It decreases the amplitude

• It increases the period

• It reflects the graph over the x-axis

• It shifts the graph up

If the function y = sin(2x) is graphed, what is its period?

• π

• 2π

• π/2

• 4π

What is the phase shift of the function y = sin(x + π/2)?

• π to the left

• π to the right

• π/2 to the left

• π/2 to the right

Which trigonometric function has vertical asymptotes?

• Cosecant

• Sine

• Cosine

• Tangent

How does the graph of cotangent differ from tangent?

• It is identical to tangent

• It rises to the right

• It has no asymptotes

• It falls to the right

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

• It is undefined

• It has vertical asymptotes

• It has peaks

• It has troughs