6.7-6.11 Review, Precal

Front

What is the amplitude of a sine function?

Back

The amplitude is the maximum distance from the midline to the peak (or trough) of the graph. It is represented by the coefficient in front of the sine function.

Front

What does the phase shift in a sine function represent?

Back

The phase shift is the horizontal shift left or right for the graph of the function. It is represented by the value 'c' in the function y = a*sin(b(x-c))+d.

Front

How do you determine the midline of a sinusoidal function?

Back

The midline is the horizontal line that runs through the middle of the graph, calculated as y = d in the function y = a*sin(b(x-c))+d.

Front

What is the period of a sine or cosine function?

Back

The period is the distance along the x-axis for one complete cycle of the wave, calculated as (2π)/|b| in the function y = a*sin(bx) or y = a*cos(bx).

Front

What is the effect of changing the coefficient 'a' in a sine function?

Back

Changing the coefficient 'a' affects the amplitude of the function. A larger 'a' results in a taller wave, while a smaller 'a' results in a shorter wave.

Front

What is the effect of changing the coefficient 'b' in a sine function?

Back

Changing the coefficient 'b' affects the period of the function. A larger 'b' results in a shorter period (more cycles in a given interval), while a smaller 'b' results in a longer period.

Front

What is the formula for the period of the function y = 5cos(⅕x)?

Back

The period is calculated as (2π)/|b|, where b = ⅕, resulting in a period of 10π.

Front

What is the difference between sine and cosine functions?

Back

Sine functions start at the midline and go up, while cosine functions start at the maximum value. This results in a phase shift of π/2 between the two functions.

Front

How do you identify the maximum and minimum values of a sine function?

Back

The maximum value is 'a + d' and the minimum value is '-a + d' in the function y = a*sin(b(x-c))+d.

Front

What is the significance of the vertical shift 'd' in a sine function?

Back

The vertical shift 'd' moves the entire graph up or down, affecting the midline of the function.