Trigonometric Functions and Their Graphs

The video tutorial demonstrates how to sketch graphs of sinusoidal functions using transformations. It covers three examples: y = 3 sin 2x, y = 4 cos(1/2)x - 2, and y = -3 sin 4x - 30° + 1. Each example explains how to determine amplitude, period, and transformations such as vertical and horizontal translations. The tutorial emphasizes using key points to plot the graphs accurately.

What is the amplitude of the function y = 3 sin 2x?

• 3

• 2

• 4

• 1

How does the '2' in y = 3 sin 2x affect the graph?

• It reflects the graph

• It shifts the graph vertically

• It halves the period

• It doubles the amplitude

Where does the graph of y = 3 sin 2x complete one full cycle?

• 180°

• 90°

• 360°

• 270°

What is the period of the function y = 4 cos(1/2)x - 2?

• 540°

• 720°

• 360°

• 180°

How does the '-2' in y = 4 cos(1/2)x - 2 affect the graph?

• It shifts the graph up

• It shifts the graph down

• It changes the amplitude

• It reflects the graph

What is the effect of the negative sign in y = -3 sin 4x - 30° + 1?

• It changes the period

• It reflects the graph across the x-axis

• It shifts the graph down

• It shifts the graph up

What is the period of the function y = -3 sin 4x - 30° + 1?

• 360°

• 90°

• 180°

• 270°

How does the '+1' in y = -3 sin 4x - 30° + 1 affect the graph?

• It shifts the graph up

• It shifts the graph down

• It changes the amplitude

• It reflects the graph

What is the horizontal shift in the function y = -3 sin 4x - 30° + 1?

• 60° to the left

• 30° to the right

• 60° to the right

• 30° to the left

What is the amplitude of the function y = -3 sin 4x - 30° + 1?

• 4

• 1

• 2

• 3