Writing Equations of Sine and Cosine

What is the effect of changing the value of B in the function y = sin(Bx)?

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

• Changing B affects the period of the function; a larger B results in a shorter period.

• Changing B affects the phase shift of the function; a larger B results in a rightward shift.

• Changing B has no effect on the function; it remains the same regardless of B.

What is the equation of the graph with an amplitude of 5 and a midline at y = 1?

• y = 5sin(x) + 1

• y = 3sin(x) + 1

• y = 5cos(x) - 1

• y = 2sin(x) + 1

What is the relationship between sine and cosine functions?

• Sine and cosine functions are phase-shifted versions of each other; sin(x) = cos(x - π/2).

• Sine and cosine functions are identical and can be used interchangeably.

• Sine is the derivative of cosine, and cosine is the integral of sine.

• Sine and cosine functions are unrelated and represent different types of waveforms.

How do you identify the phase shift in the function y = sin(x - π/2)?

• The phase shift is π/2 to the left.

• The phase shift is π/2 to the right.

• The phase shift is π to the right.

• There is no phase shift.

How do you determine the period of a sine or cosine function?

• The period is calculated as 2π/B, where B is the coefficient of x in the function.

• The period is calculated as π/B, where B is the coefficient of x in the function.

• The period is calculated as 2π/B^2, where B is the coefficient of x in the function.

• The period is calculated as B/2π, where B is the coefficient of x in the function.

What is the amplitude of a sine or cosine function?

• 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 midline and the x-axis.

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

How do you find the midline of the function y = 3sin(x) - 2?

• y = 3

• y = 0

• y = -2

• y = 2

What is the midline of a sine or cosine graph?

• The midline is the horizontal line that runs through the middle of the graph, representing the average value of the function.

• The midline is the highest point of the graph where the function reaches its maximum value.

• The midline is the vertical line that divides the graph into two equal halves.

• The midline is the point where the graph intersects the x-axis.

What does a negative amplitude indicate in a sine or cosine function?

• A negative amplitude reflects the graph across the midline.

• A negative amplitude indicates a phase shift to the left.

• A negative amplitude results in a vertical stretch of the graph.

• A negative amplitude causes the graph to oscillate faster.

What is the general form of a sine function?

• y = A sin(B(x - C)) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the midline.

• y = A cos(B(x - C)) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the midline.

• y = A tan(B(x - C)) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the midline.

• y = A sin(Bx) + D, where A is the amplitude, B affects the frequency, and D is the vertical shift.