How do we recognize and graph periodic and trigonometric functions?

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How do we recognize and graph periodic and trigonometric functions? Graphs of Sine and Cosine Essential Questions How do we recognize and graph periodic and trigonometric functions? Holt McDougal Algebra 2 Holt Algebra 2

Sine and cosine functions can be used to model real-world phenomena, such as sound waves. Different sounds create different waves. One way to distinguish sounds is to measure frequency. Frequency is the number of cycles in a given unit of time, so it is the reciprocal of the period of a function. Hertz (Hz) is the standard measure of frequency and represents one cycle per second. For example, the sound wave made by a tuning fork for middle A has a frequency of 440 Hz. This means that the wave repeats 440 times in 1 second.

Amplitude: Period: Frequency: Sound Application Use a sine function to graph a sound wave with a period of 0.002 s and an amplitude of 3 cm. Find the frequency in hertz for this sound wave. Amplitude: Period: Frequency: The frequency of the sound wave is 500 Hz.

Amplitude: Period: Frequency: Sound Application Use a sine function to graph a sound wave with a period of 0.004 s and an amplitude of 3 cm. Find the frequency in hertz for this sound wave. Amplitude: Period: Frequency: The frequency of the sound wave is 250 Hz.

Employment Application The number of people, in thousands, employed in a resort town can be modeled by, month of the year. A. Graph the number of people employed in the town for one complete period. Amplitude: Period: Translation: left 2, up 5.2 B. What is the maximum number of people employed?

Employment Application Suppose that the height H, in feet of a Ferris wheel can be modeled by, A. Graph the height of the cabin for one complete period. Amplitude: Period: Translation: up 24 What is the minimum height of the cabin on the Ferris Wheel?

Lesson 11.1 Practice C