8.3 Graphing Trig Functions Practice

Front

What is the period of a trigonometric function?

Back

The period is the length of one complete cycle of the function. For sine and cosine functions, the standard period is 2π.

Front

How do you determine the amplitude of a trigonometric function?

Back

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

Front

Write the equation for a cosine function with amplitude 3, period 2π, phase shift of π, and vertical shift of 5.

Back

y = 3cos(x - π) + 5

Front

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

Back

The amplitude is 5.

Front

Where does the graph of y = cos x begin?

Back

The graph begins at the point (0, 1).

Front

What is the phase shift in the function y = cos(x - π)?

Back

The phase shift is π to the right.

Front

How do you find the vertical shift of a trigonometric function?

Back

The vertical shift is determined by the constant added or subtracted from the function. For example, in y = sin(x) + 2, the vertical shift is 2 units up.

Front

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

Back

The period is 2π/3.

Front

If the amplitude of a sine function is 4, what is the maximum value of the function?

Back

The maximum value is 4.

Front

What is the general form of a cosine function?

Back

The general form is y = A cos(B(x - C)) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.