Graphing Trigonometric Functions

The video tutorial covers the six trigonometric functions, focusing on their domains, ranges, and periodicity. It explains how to graph sine and cosine functions, including transformations like amplitude changes and shifts. The tutorial also discusses the characteristics and graphing of tangent, cotangent, secant, and cosecant functions, highlighting their unique features such as asymptotes and periodicity.

What is the range of the sine function?

• -infinity to infinity

• 0 to infinity

• All real numbers

• -1 to 1 inclusive

Which trigonometric function has a domain of all real numbers except for specific points where cosine is zero?

• Secant

• Tangent

• Cosine

• Sine

What is the period of the sine and cosine functions?

• 4 pi radians

• 2 pi radians

• Pi radians

• 3 pi radians

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

• It stretches the graph vertically

• It compresses the graph horizontally

• It reflects the graph across the x-axis

• It shifts the graph vertically

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

• 4

• 1

• 2

• 3

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

• It has a larger amplitude

• It has a smaller amplitude

• It has a longer period

• It has a shorter period

What is the phase shift of the function y = sin(x + pi/4)?

• Pi/4 to the right

• Pi/4 to the left

• Pi/2 to the left

• Pi/2 to the right

Which trigonometric function has vertical asymptotes where cosine is zero?

• Sine

• Cosine

• Tangent

• Cosecant

What is the period of the tangent function?

• 4 pi radians

• Pi radians

• 2 pi radians

• 3 pi radians

How does the graph of cotangent differ from tangent?

• It rises to the right

• It has a longer period

• It falls to the right

• It has no asymptotes