Amplitude and Period

Front

What is the definition of amplitude in a periodic function?

Back

Amplitude is the maximum distance from the midline (equilibrium position) of the wave to its peak (or trough). It represents the height of the wave.

Front

How do you find the amplitude of a sine or cosine function?

Back

The amplitude can be found by taking the absolute value of the coefficient in front of the sine or cosine function. For example, in y = A sin(x), the amplitude is |A|.

Front

What is the period of a periodic function?

Back

The period is the length of one complete cycle of the wave. It is the distance along the x-axis after which the function repeats itself.

Front

How do you calculate the period of a sine or cosine function?

Back

The period can be calculated using the formula: Period = 2π / |B|, where B is the coefficient of x in the function y = A sin(Bx) or y = A cos(Bx).

Front

What is the amplitude of the function y = 5 sin(x)?

Back

5

Front

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

Back

3 (amplitude is always positive, so we take the absolute value).

Front

What is the period of the function y = sin(2x)?

Back

π (since the period is calculated as 2π / |2| = π).

Front

What is the period of the function y = cos(0.5x)?

Back

4π (since the period is calculated as 2π / |0.5| = 4π).

Front

If the function is y = 2 sin(3x), what is the amplitude?

Back

2

Front

If the function is y = 4 cos(5x), what is the period?

Back

2π/5 (since the period is calculated as 2π / |5| = 2π/5).