Graphing Trig Functions

Front

What is the amplitude of a trigonometric function?

Back

The amplitude is the maximum distance from the midline of the graph to the peak (or trough) of the wave. It is always a positive value.

Front

How do you determine the amplitude from the equation y = A sin(Bx) or y = A cos(Bx)?

Back

The amplitude is given by the absolute value of A. For example, in y = -10cos(5x), the amplitude is | -10 | = 10.

Front

What is the period of a trigonometric function?

Back

The period is the distance along the x-axis for one complete cycle of the wave. It can be calculated using the formula: Period = 2π / |B|.

Front

How do you find the period from the equation y = A sin(Bx) or y = A cos(Bx)?

Back

The period is calculated as 2π divided by the absolute value of B. For example, in y = -3sin(7x), the period is 2π / 7.

Front

What is a vertical shift in a trigonometric function?

Back

A vertical shift moves the graph up or down on the y-axis. It is determined by the constant added or subtracted from the function.

Front

How do you identify a vertical shift from the equation y = A sin(Bx) + D?

Back

The vertical shift is represented by D. If D is positive, the graph shifts up; if negative, it shifts down.

Front

What is the difference between sine and cosine functions?

Back

Sine functions start at the midline (0) and go up, while cosine functions start at the maximum value (A) and go down.

Front

What is the general form of a sine function?

Back

The general form is y = A sin(Bx + C) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

Front

What is the general form of a cosine function?

Back

The general form is y = A cos(Bx + C) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

Front

How does a negative amplitude affect the graph of a trigonometric function?

Back

A negative amplitude reflects the graph across the midline, effectively flipping it upside down.