Trigonometric Graphs and Their Properties

The video tutorial covers the analysis of tan and sin graphs, focusing on determining the period of a sin graph, calculating the K value, and finding intersection points. It also explains how to determine the range of a graph with a multiplier and compares expressions to find where one graph is smaller than another. Finally, it addresses solving for P in an equation to find real roots, emphasizing time management during exams.

What type of graph is represented by f(x) in the problem?

• Cosine graph

• Tangent graph

• Sine graph

• Linear graph

What is the period of a tangent graph?

• 270°

• 90°

• 180°

• 360°

What is the period of a cosine graph?

• 90°

• 270°

• 360°

• 180°

What is the period of a standard sine graph?

• 90°

• 270°

• 180°

• 360°

How do you calculate the period of a transformed sine graph?

• Subtract K from the original period

• Multiply the original period by K

• Divide the original period by K

• Add K to the original period

How do you determine the period of a tangent graph?

• Add K to the original period

• Multiply the original period by K

• Divide the original period by K

• Subtract K from the original period

What is the effect of a coefficient on the period of a sine graph?

• It doubles the period

• It shifts the period down

• It halves the period

• It shifts the period up

How do you determine the period of a cosine graph?

• Subtract K from the original period

• Divide the original period by K

• Multiply the original period by K

• Add K to the original period

What is the effect of a negative coefficient on the period of a sine graph?

• It halves the period

• It shifts the period up

• It doubles the period

• It inverts the period

What is the period of a sine graph with a coefficient of 3?

• 360°

• 270°

• 180°

• 120°