12.7Graphing 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 θ2. 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

Find the amplitude and period of

Example 1b

Find the amplitude and period of

Example 2

Find the amplitude and period. Then find a possible equation in the form of or for the function.

Example 3

Find the amplitude and period. Then find a possible equation in the form of or for the function.

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.