Understanding Sine and Cosine Graphs

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

• π/2

• 2π

• 3π

• π

How do you find the midpoint between 0 and 2π when sketching sine and cosine graphs?

• Add π

• Divide by 3

• Cut in half

• Multiply by 2

What does multiplying a sine or cosine function by a number affect?

• Period

• Amplitude

• Frequency

• Phase shift

If the amplitude of a sine function is 2, what is the range of the function?

• 0 to 2

• -1 to 1

• -3 to 3

• -2 to 2

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

• 1

• 0

• 3

• -3

What is the maximum value of the function y = 3sin(x)?

• -3

• 3

• 1

• 0

In the function y = 2sin(x), what does the '2' represent?

• Phase shift

• Amplitude

• Frequency

• Period

What happens to the graph of y = cos(x) when the amplitude is increased to 4?

• It shifts horizontally

• It compresses vertically

• It stretches vertically

• It remains unchanged

How is the amplitude of a periodic function formally defined?

• Twice the max value

• Half the difference between max and min values

• The sum of max and min values

• The average of max and min values

If the amplitude of a cosine function is 5, what is the total vertical distance covered by one cycle?

• 2.5

• 0

• 10

• 5