Math 4 Unit 4 Review

Front

What is the definition of amplitude in a trigonometric function?

Back

Amplitude is the maximum distance from the midline of the graph to the peak (or trough) of the wave. It is half the distance between the maximum and minimum values of the function.

Front

How do you determine the amplitude of the function f(x) = A sin(Bx) + D or f(x) = A cos(Bx) + D?

Back

The amplitude is the absolute value of A. For example, in f(x) = -3sin(7x) - 2, the amplitude is | -3 | = 3.

Front

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

Back

The period of a sine or cosine function is given by the formula: Period = 2π / |B|, where B is the coefficient of x in the function.

Front

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

Back

The period is 2π / 3.

Front

What does the variable D represent in the function f(x) = A sin(Bx) + D?

Back

D represents the vertical shift of the graph. It moves the graph up or down without affecting the amplitude or period.

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, multiply the degree measure by π/180.

Front

What is 225 degrees in radians?

Back

225 degrees is equal to 5π/4 radians.

Front

What is the relationship between the maximum and minimum values of a sine or cosine function?

Back

The maximum value is D + A and the minimum value is D - A, where A is the amplitude and D is the vertical shift.

Front

How can you identify the amplitude from the graph of a sine or cosine function?

Back

The amplitude can be identified by measuring the distance from the midline of the graph to the highest or lowest point.

Front

What is the effect of changing the value of A in the function f(x) = A sin(Bx) + D?

Back

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