Sine and Cosine - Amplitude and Period

Define 'period' in the context of sine and cosine graphs.

• The vertical distance between the maximum and minimum points of the graph.

• The horizontal length required to complete one full cycle of the graph.

• The rate at which the graph oscillates up and down.

• The amplitude of the sine and cosine functions.

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

• @@rac{2 ext{π}}{b}@@, where b is the coefficient of x in the function.

• @@2 ext{π}b@@, where b is the coefficient of x in the function.

• @@rac{b}{2 ext{π}}@@, where b is the coefficient of x in the function.

• @@rac{1}{b}@@, where b is the coefficient of x in the function.

How does the value of 'b' affect the period of the sine and cosine functions?

• The period is given by @@rac{2 ext{π}}{b}@@, determining how many cycles occur in a given interval.

• The value of 'b' has no effect on the period of the sine and cosine functions.

• The period is always 2π regardless of the value of 'b'.

• The value of 'b' only affects the amplitude of the sine and cosine functions.

What is the maximum value of the function y = 4cos(x)?

• 2

• 3

• 4

• 5

What is the phase shift in the function y = sin(bx + c)?

• The phase shift is determined by the value of c; it shifts the graph horizontally.

• The phase shift is determined by the value of b; it stretches the graph vertically.

• The phase shift is determined by the amplitude of the function; it affects the height of the graph.

• The phase shift is always zero regardless of the values of b and c.

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

• π

• 2π

• 3π

• 4π

What is the amplitude of a sine or cosine graph?

• The amplitude is the maximum distance from the midline to the peak (or trough) of the graph.

• The amplitude is the horizontal distance between two consecutive peaks.

• The amplitude is the vertical distance between the highest and lowest points of the graph.

• The amplitude is the rate of change of the graph over time.

What is the difference between sine and cosine functions?

• Sine functions start at the maximum value (amplitude) at x=0, while cosine functions start at the midline (0) and go down.

• Sine functions start at the midline (0) and go up, while cosine functions start at the maximum value (amplitude) at x=0.

• Sine functions and cosine functions are identical and have no differences.

• Sine functions are only defined for positive angles, while cosine functions are defined for all angles.

What is the general form of a sine function?

• y = a sin(bx + c) + d

• y = a cos(bx + c) + d

• y = a tan(bx + c) + d

• y = a sin(bx) + d

What is the vertical shift in the function y = a sin(bx) + d?

• The vertical shift is determined by the value of a; it stretches the graph vertically.

• The vertical shift is determined by the value of b; it affects the frequency of the graph.

• The vertical shift is determined by the value of d; it moves the graph up or down.

• The vertical shift is determined by the amplitude of the function; it affects the height of the peaks.