Modeling w/Trig Functions Homework

Front

What is the amplitude of a trigonometric function?

Back

The amplitude is the maximum distance from the midline of the graph to its highest or lowest point. For a function of the form y = A sin(Bx), the amplitude is |A|.

Front

How do you find the vertical shift of a trigonometric function?

Back

The vertical shift is found by determining the midline of the function, which is the average of the maximum and minimum values.

Front

What is the formula for the period of a sine function?

Back

Front

What does the term 'angular frequency' refer to in trigonometric functions?

Back

Angular frequency (b) indicates how many cycles occur in a unit of time and is related to the period of the function.

Front

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

Back

For a function of the form y = A sin(Bx) + D, the maximum value is D + |A| and the minimum value is D - |A|.

Front

What is the initial value of a trigonometric function?

Back

The initial value is the value of the function at the starting point, usually when x = 0.

Front

What is the significance of the string length in modeling the height of a yo-yo with a trigonometric function?

Back

The string length determines the maximum height the yo-yo can reach, which affects the amplitude of the function.

Front

How do you calculate the period of a function given the time it takes to complete one cycle?

Back

The period is the total time taken for one complete cycle of the function.

Front

What is the relationship between the period and the frequency of a trigonometric function?

Back

Front

What is the formula for the population model of a species using sine functions?

Back

A population model can be expressed as P(t) = D + A sin(Bt), where D is the vertical shift, A is the amplitude, and B relates to the period.