Amplitude and Range of Trigonometric Functions

The video tutorial explains the concept of amplitude in trigonometric functions, specifically sine and cosine. It discusses how amplitude affects the range of these functions, which is typically between -1 and 1. By multiplying the function by a number, the range is altered, and the amplitude is defined as the absolute value of this number. The tutorial provides examples to illustrate how different amplitudes affect the graph of the cosine function, showing how the function's range expands or contracts. It also demonstrates how to calculate amplitude, emphasizing that it is always a positive value.

What is the amplitude of a trigonometric function?

• The range of the function

• The absolute value of the coefficient of the function

• The period of the function

• The maximum value of the function

What is the range of the sine and cosine functions?

• 0 to 2

• -2 to 2

• -1 to 1

• 0 to 1

How does multiplying a sine or cosine function by a number affect its range?

• It reflects the graph over the x-axis

• It changes the period of the function

• It shifts the graph horizontally

• It affects the range by scaling it

What happens to the graph of y = 2cos(x)?

• The graph is reflected over the y-axis

• The period is halved

• The amplitude is doubled, making the range -2 to 2

• The graph is shifted up by 2 units

If y = -3cos(x), what is the amplitude?

• 1

• 3

• -3

• 0

What is the amplitude of y = 1/4sin(x)?

• 0

• 1

• 1/4

• 4

How does the amplitude affect the graph of a trigonometric function?

• It changes the period

• It changes the vertical stretch or compression

• It reflects the graph over the x-axis

• It shifts the graph horizontally

What is the effect of an amplitude less than 1 on the graph of a trigonometric function?

• The graph is shifted up

• The graph is shifted down

• The graph is compressed vertically

• The graph is stretched vertically

In the function y = a sin(x), what does 'a' represent?

• The frequency

• The amplitude

• The phase shift

• The period of the function

What is the range of y = 3cos(x)?

• -3 to 3

• -2 to 2

• -1 to 1

• 0 to 3