Graphing Sine and Cosine Functions

The video tutorial covers the concepts of frequency, wavelength, and period in wave graphs, focusing on sine and cosine functions. It explains how amplitude affects graph shape and how transformations can stretch graphs. The tutorial details how to find period and frequency from equations and graphs, and provides techniques for graphing waves with different periods and amplitudes. It also includes methods for analyzing graphs to determine equations and characteristics, concluding with a recap of key concepts.

What effect does a multiplier in front of the sine function have on the graph?

• It makes the graph wider.

• It makes the graph taller.

• It shifts the graph vertically.

• It shifts the graph horizontally.

What happens to the graph of y = sin(x) when the input variable x is multiplied?

• The graph shifts downwards.

• The graph becomes wider.

• The graph becomes thinner.

• The graph shifts upwards.

What is the period of the function y = sin(2x)?

• 2π

• 4π

• π/2

• π

How is frequency defined in the context of wave graphs?

• The number of waves completed in one unit of time.

• The distance between two peaks.

• The height of the wave.

• The width of the wave.

What is the frequency of a wave with a period of 2π?

• 2π

• 1/π

• 1/2π

• π

For the function y = sin(4x), what is the period?

• 2π

• π

• 4π

• π/2

What is the general formula for the period of a sine wave?

• 2π/B

• B/π

• π/B

• B/2π

How do you determine the quarter markings when graphing y = sin(5x)?

• Divide the period into 3 equal parts.

• Divide the period into 4 equal parts.

• Divide the period into 5 equal parts.

• Divide the period into 6 equal parts.

What is the amplitude of the function y = −2 cos(3x)?

• 3

• 4

• 1

• 2

How does a negative sign in front of a cosine function affect its graph?

• It flips the graph left to right.

• It shifts the graph upwards.

• It shifts the graph downwards.

• It flips the graph top to bottom.