Trig Functions Amplitude and Period

Front

What is Amplitude?

Back

Amplitude is the distance from the midline to the maximum or minimum value of a periodic function.

Front

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

Front

What is the period of y=4cos5x?

Back

The period is 2π/5.

Front

What does the term 'Vertical Translation' refer to in trigonometric functions?

Back

Vertical Translation refers to shifting the graph of a function up or down along the y-axis.

Front

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

Back

The normal period is 2π.

Front

What does 'Phase Shift' mean in trigonometric functions?

Back

Phase Shift refers to the horizontal shift left or right for periodic functions.

Front

What is the difference between Amplitude and Period?

Back

Amplitude measures the height of the wave from the midline, while Period measures the length of one complete cycle of the wave.

Front

What is the maximum value of the function y=3sin(x)?

Back

The maximum value is 3, which is the amplitude of the function.

Front

What is the minimum value of the function y=3cos(x)?

Back

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

Front

What is the effect of increasing the amplitude of a sine function?

Back

Increasing the amplitude stretches the graph vertically, making the peaks and troughs higher and lower.