4e Example 1 (How to Graph the Sine Function)

The video tutorial covers graphing and identifying characteristics of sine and cosine graphs, including period, phase shift, vertical shift, range, and reflections. It explains transformations and provides examples using Desmos for visualization. The tutorial also discusses amplitude and how to sketch graphs with transformations, emphasizing understanding of range and domain.

What is the primary focus when graphing sine and cosine functions?

• Identifying the x-intercepts

• Identifying the range

• Identifying the domain

• Identifying key characteristics like period and phase shift

How is the period of a sine function calculated?

• π times B

• π divided by B

• 2π divided by B

• 2π times B

What does a phase shift in a sine function indicate?

• A vertical shift

• A horizontal shift

• A change in amplitude

• A reflection over the x-axis

What is the range of a sine function with no vertical shift and an amplitude of 1?

• From 0 to 1

• From -2 to 2

• From 0 to 2

• From -1 to 1

What happens to the period of a sine function when B is 2?

• It doubles

• It halves

• It remains the same

• It triples

What is the amplitude of a sine function with an 'a' value of 1/3?

• 1

• 1/3

• 3

• 2/3

How does a negative sign inside the sine function affect the graph?

• It compresses the graph horizontally

• It shifts the graph vertically

• It reflects the graph over the y-axis

• It reflects the graph over the x-axis

What is the range of a sine function with an amplitude of 2 and a vertical shift of -2?

• From 0 to 4

• From -2 to 2

• From -1 to 1

• From -4 to 0

What is the effect of a negative sign outside the sine function?

• It stretches the graph vertically

• It reflects the graph over the y-axis

• It reflects the graph over the x-axis

• It shifts the graph horizontally

How does the initial point of a cosine function differ from that of a sine function?

• Cosine starts at (0,0)

• Cosine starts at (0,1)

• Cosine starts at (1,0)

• Cosine starts at (1,1)