Trigonometric Functions and Graphs

The video tutorial covers the basics of trigonometric graphing, focusing on amplitude and period changes. It begins with an introduction to these concepts, followed by examples using sine and cosine functions. The first example demonstrates how the amplitude of y=4sin(theta) changes, while the second example shows how the period of y=sin(3theta) is affected. Finally, the tutorial combines both amplitude and period changes in the function y=2cos(1/3theta), illustrating how these transformations impact the graph's shape and cycle.

What is the primary focus of trigonometric graphing discussed in the introduction?

• Amplitude and frequency

• Amplitude and period

• Period and phase shift

• Frequency and phase shift

In the example y = 4 sin(theta), what is the amplitude of the graph?

• 4

• 3

• 2

• 1

How does the amplitude affect the sine graph in y = 4 sin(theta)?

• It compresses the graph horizontally

• It stretches the graph vertically

• It shifts the graph horizontally

• It reflects the graph over the x-axis

What is the period of the function y = sin(3 theta)?

• 360 degrees

• 180 degrees

• 90 degrees

• 120 degrees

How does the b value in y = sin(3 theta) affect the period?

• It doubles the period

• It halves the period

• It triples the period

• It reduces the period by a factor of 3

In the function y = 2 cos(1/3 theta), what is the amplitude?

• 4

• 2

• 3

• 1

What is the period of y = 2 cos(1/3 theta)?

• 1440 degrees

• 1080 degrees

• 720 degrees

• 360 degrees

How does the cosine graph start and end in a full cycle?

• Starts at maximum, ends at maximum

• Starts at zero, ends at zero

• Starts at zero, ends at maximum

• Starts at minimum, ends at minimum

What is the effect of changing the amplitude on a trigonometric graph?

• It changes the phase shift

• It changes the horizontal shift

• It changes the vertical stretch

• It changes the period

What is the effect of changing the b value on a trigonometric graph?

• It changes the vertical shift

• It changes the period

• It changes the amplitude

• It changes the phase shift