Understanding Sine and Cosine Functions

The video tutorial covers the concepts of amplitude and period in sine and cosine graphs. It explains how to graph these functions, focusing on the effects of changing the amplitude and period. The tutorial includes examples of graphing y = 3 sin(2x) and a cosine function, highlighting the impact of amplitude, period, and reflection. The video concludes with recommendations for further practice.

What is the general form of a sine or cosine graph?

• y = a sin(bx + c) + d

• y = a sin(bx) + c

• y = a cos(bx) + c

• y = sin(ax + b) + d

How does increasing the value of 'a' affect the graph of a sine function?

• It reflects the graph over the x-axis.

• It compresses the graph horizontally.

• It stretches the graph vertically.

• It shifts the graph horizontally.

What happens to the period of a sine graph as the value of 'b' increases?

• The period becomes longer.

• The graph reflects over the y-axis.

• The period remains the same.

• The period becomes shorter.

If a sine function has an amplitude of 3 and a period of π, what is the value of 'b'?

• 2

• 1

• 4

• 3

What is the frequency of a sine function with a period of π?

• 1

• 1/π

• π

• 2π

In a cosine graph, what does a negative amplitude indicate?

• The graph is stretched horizontally.

• The graph is compressed vertically.

• The graph is reflected over the x-axis.

• The graph is shifted up.

What is the period of a cosine function with b = 1/2?

• 4π

• 2π

• π

• 8π

How is the frequency of a periodic function related to its period?

• Frequency is twice the period.

• Frequency is the reciprocal of the period.

• Frequency is half the period.

• Frequency is the square of the period.

What is the effect of a negative 'a' value on the graph of a sine function?

• It stretches the graph vertically.

• It compresses the graph horizontally.

• It reflects the graph over the x-axis.

• It shifts the graph to the right.

What is the amplitude of the function y = -2 cos(x/2)?

• 1

• 4

• 2

• 1/2