Midline, Amplitude, and Period of Trig Functions

Front

What is the definition of the midline in a trigonometric function?

Back

The midline is the horizontal line that runs through the middle of the maximum and minimum values of the function, representing the average value of the function.

Front

How do you determine the amplitude of a trigonometric function?

Back

The amplitude is the distance from the midline to the maximum (or minimum) value of the function.

Front

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

Back

The period can be found 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

If a trigonometric function has a maximum value of 5 and a minimum value of -1, what is the amplitude?

Back

The amplitude is (5 - (-1)) / 2 = 3.

Front

What is the period of the function y = 3 sin(2x)?

Back

The period is 2π / 2 = π.

Front

What does a negative amplitude indicate in a trigonometric function?

Back

A negative amplitude does not have a physical meaning; amplitude is always a non-negative value. A negative sign indicates a reflection over the midline.

Front

How can you find the midline of the function y = 2 sin(x) - 3?

Back

The midline is y = -3, which is the vertical shift of the function.

Front

What is the effect of changing the coefficient 'a' in the function y = a sin(x)?

Back

Changing 'a' affects the amplitude of the function; a larger 'a' results in a taller wave.

Front

If the function y = 4 cos(x) has a maximum value of 4, what is its amplitude?

Back

The amplitude is 4.

Front

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

Back

The period is 2π / 3.