Practice: Identifying Period only from a Graph

Front

What is the definition of the period of a periodic function?

Back

The period of a periodic function is the smallest positive value of x for which the function repeats its values, typically denoted as T.

Front

How do you determine the period of a sine function?

Back

The period of a sine function is given by the formula T = \frac{360}{|b|} for the function y = a \sin(bx + c) + d.

Front

How do you determine the period of a cosine function?

Back

The period of a cosine function is given by the formula T = \frac{360}{|b|} for the function y = a \cos(bx + c) + d.

Front

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

Back

The period is T = \frac{360}{2} = 180\degree.

Front

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

Back

The period is T = \frac{360}{3} = 120\degree.

Front

What is the period of the function y = \sin(\frac{1}{2}x)?

Back

The period is T = \frac{360}{\frac{1}{2}} = 720\degree.

Front

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

Back

The period is T = \frac{360}{4} = 90\degree.

Front

If a function has a period of 360\degree, what does this imply?

Back

It implies that the function completes one full cycle every 360\degree.

Front

What is the relationship between the period and frequency of a periodic function?

Back

The frequency is the reciprocal of the period; frequency = \frac{1}{T}.

Front

How can you visually identify the period of a function from its graph?

Back

The period can be identified by measuring the distance along the x-axis between two consecutive peaks or troughs.