How does the period affect the sine and cosine graph

The video tutorial explains the concepts of cosine and sine functions, focusing on their periods. It discusses how the period of these functions is 2π and how multiplying the variable inside the function can alter the period. The tutorial demonstrates graphing both cosine and sine functions with altered periods, highlighting the changes in critical points and the overall shape of the graphs.

What is the period of the basic sine and cosine functions?

• π

• 2π

• π/2

• 4π

How can the period of a trigonometric function be altered?

• By subtracting a constant from the function

• By adding a constant to the function

• By multiplying the variable inside the function by a constant

• By multiplying the function by a constant

What is the formula to determine the period of a trigonometric function?

• π / a

• 2π / b

• π / b

• 2π / a

When graphing a cosine function with a modified period, how do you determine the new critical points?

• Divide the new period by 2

• Add π to the new period

• Multiply the new period by 4

• Divide the new period by 4

What happens to the cosine graph when the period is reduced to π?

• The graph stretches

• The graph flips

• The graph shrinks

• The graph remains unchanged

In the sine function with a period of 4π, where is the first maximum point located?

• At 3π

• At 2π

• At π

• At π/2

How does the sine graph change when the period is extended to 4π?

• The graph remains unchanged

• The graph flips

• The graph shrinks

• The graph stretches