Math 3 Unit 8 Lesson 5 Review

Front

What is the amplitude of a sine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. It represents half the distance between the maximum and minimum values of the function.

Front

Write the equation for a sine function with an amplitude of 6 and a period of \(\frac{\pi}{4}\).

Back

The equation is \(y = 6\sin(8x)\).

Front

What is the period of the function \(y = -3 \sin(x)\)?

Back

The period is \(2\pi\).

Front

In the function \(y = A\sin(B(x-h)) + k\), what does \(B\) represent?

Back

The value \(B\) affects the period of the sine function, which is calculated as \(\frac{2\pi}{B}\).

Front

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

Back

The period is given by the formula \(\frac{2\pi}{B}\).

Front

What does the term 'frequency' refer to in the context of sine functions?

Back

Frequency is the number of cycles a sine function completes in a unit interval, calculated as \(\frac{1}{\text{Period}}\).

Front

What is the amplitude of the function \(y = -5\sin(2(x+4)) + 6\)?

Back

The amplitude is 5.

Front

Describe the transformations of the function \(y = -5\sin(2(x+4)) + 6\).

Back

The function has an amplitude of 5, a period of \(\pi\), a left shift of 4 units, and an upward shift of 6 units.

Front

What is the maximum value of the function \(y = 6\sin(x)\)?

Back

The maximum value is 6, which is the amplitude of the function.

Front

What is the minimum value of the function \(y = -3\sin(x)\)?

Back

The minimum value is 3, which is the negative of the amplitude.