Midline, Amplitude, and Period of Trig Functions

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

• π

• 2π

• 2π / 3

• 3π

How can you graph a trigonometric function using its amplitude, period, and midline?

• Start by plotting the midline, then mark the maximum and minimum points based on the amplitude, and finally use the period to determine the x-values for one complete cycle.

• Begin by determining the amplitude, then sketch the graph without considering the midline or period.

• Plot the maximum and minimum points first, then draw the midline, and finally adjust for the period.

• Use the period to find the midline, then plot the amplitude, and finally connect the points with a straight line.

What does a negative amplitude indicate in a trigonometric function?

• A negative amplitude indicates a reflection over the midline.

• A negative amplitude has a physical meaning in trigonometric functions.

• A negative amplitude is always a positive value.

• A negative amplitude indicates a phase shift.

What is the midline of the function y = 5 sin(x) + 2?

• y = 0

• y = 2

• y = 5

• y = -2

If the function y = 4 cos(x) has a maximum value of 4, what is its amplitude?

• 2

• 3

• 4

• 5

What is the period of the function y = 3 sin(2x)?

• π

• 2π

• π/2

• 3π

What is the effect of changing the coefficient 'a' in the function y = a sin(x)?

• It affects the frequency of the function; a larger 'a' results in a faster wave.

• Changing 'a' affects the amplitude of the function; a larger 'a' results in a taller wave.

• It has no effect on the function; the wave remains the same regardless of 'a'.

• It affects the phase shift of the function; a larger 'a' shifts the wave to the right.

What is the relationship between the amplitude and the vertical shift of a trigonometric function?

• The amplitude determines the height of the wave, while the vertical shift moves the midline up or down without affecting the amplitude.

• The amplitude and vertical shift are the same concept in trigonometric functions.

• The vertical shift determines the height of the wave, while the amplitude moves the midline up or down.

• The amplitude affects the frequency of the wave, while the vertical shift affects the phase.

If a trigonometric function has a maximum value of 5 and a minimum value of -1, what is the amplitude?

• 2

• 3

• 4

• 5

What is the formula to find the period of a sine or cosine function?

• Period = 2π / |b|

• Period = 2π * b

• Period = b / 2π

• Period = |b| / 2π