Phase Shifts in Sine Graphs

The video tutorial explains the features of a sine graph, focusing on frequency and phase shifts. It demonstrates how these changes affect the graph's appearance and provides two methods for graphing these transformations. Common student errors are discussed, emphasizing the importance of understanding the interaction between frequency and phase shifts. The tutorial concludes with alternative graphing methods to achieve the same results.

What is the effect of changing the frequency of a sine graph?

• It changes the graph's amplitude.

• It changes the vertical position of the graph.

• It alters the number of cycles within a given period.

• It shifts the graph horizontally.

What is another term for a horizontal shift in trigonometric functions?

• Phase shift

• Frequency shift

• Amplitude change

• Vertical shift

When applying a phase shift to a sine graph, what is a common mistake students make?

• They apply a vertical shift.

• They change the amplitude instead.

• They confuse the direction of the shift.

• They forget to label the axes.

How does the frequency change affect the period of a sine graph?

• It has no effect on the period.

• It triples the period.

• It doubles the period.

• It halves the period.

What happens to the x-intercepts of a sine graph when the frequency is doubled?

• They remain the same.

• They are expanded to double their original distance.

• They are shifted to the left.

• They are compressed to half their original distance.

In the alternative graphing method, what is the first step?

• Label the axes.

• Draw the original sine graph.

• Change the frequency.

• Apply the phase shift.

How is the phase shift shared when there are multiple cycles in a sine graph?

• It is ignored.

• It is divided equally among all cycles.

• It is doubled for each cycle.

• It is applied to only one cycle.

What is the result of applying a 90° phase shift to a sine graph with a doubled frequency?

• No shift

• A 90° shift to the left

• A 90° shift to the right

• A 45° shift to the right

What is the correct order of transformations to avoid errors in graphing?

• Vertical shift first, then frequency change

• Amplitude change first, then phase shift

• Frequency change first, then phase shift

• Phase shift first, then frequency change

What is the effect of a phase shift on the sine graph's turning points?

• They remain unchanged.

• They are removed.

• They are shifted vertically.

• They are shifted horizontally.