12.2 Amplitude and Period

Front

What is the definition of amplitude in a trigonometric function?

Back

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

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: \( T = \frac{2\pi}{|b|} \), where \( b \) is the coefficient of the variable inside the function.

Front

What is the period of the function \( y = 5\cos(6x) \)?

Back

The period is \( \frac{2\pi}{6} = \frac{\pi}{3} \).

Front

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

Back

The period is \( \frac{2\pi}{2} = \pi \).

Front

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

Back

The amplitude is 3.

Front

What is the normal period of a sine or cosine function without any dilations?

Back

The normal period is \( 2\pi \).

Front

What is the amplitude and period of \( y = 2\sin(3x) \)?

Back

The amplitude is 2 and the period is \( \frac{2\pi}{3} \).

Front

How does the coefficient of the sine or cosine function affect the amplitude?

Back

The coefficient in front of the sine or cosine function determines the amplitude. For example, in \( y = A\sin(Bx) \), the amplitude is |A|.

Front

What is the effect of changing the coefficient of x in \( y = \sin(kx) \) on the period?

Back

The period is affected by the coefficient k, calculated as \( T = \frac{2\pi}{|k|} \).

Front

What is the period of the function \( y = \cos(4x) \)?

Back

The period is \( \frac{2\pi}{4} = \frac{\pi}{2} \).