12.7 Graphing Trigonometric Functions Day 1: Sine and Cosine.

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Presentation transcript:

12.7 Graphing Trigonometric Functions Day 1: Sine and Cosine

Graph the following in your calculator. Find the period and minimum and maximum values for each function. 1. f(θ) = sin θ 2. f(θ) = cos θ

The amplitude of the graph of sine and cosine functions equals half The difference between the maximum and the minimum values.

Finding Amplitude and Period Example 1a

Example 1b

Example 2

Example 3

Applications

Example 4 Humans can hear sounds with a frequency of 40 Hz. Find the period of the function that models the sound waves. Let the amplitude equal 1 unit. Write a sine equation to represent the sound wave y as a function of time t.

Example 5 The bass tuba can produce sounds with as low a frequency as 50 Hz. Find the period of the function that models the sound waves. Let the amplitude equal 2 unit. Determine the correct cosine equation to represent the sound wave y as a function of time t.