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

Finding Amplitude and Period Example 1a

Example 1b

Graphing Trigonometric Functions O Graph the function y = sin 3 . O First, find amplitude and period O Next, find x-intercepts O Graph

Graphing Trigonometric Functions

Graphing Trigonometric Functions- You try

Applications

Application Example O SOUND Humans can hear sounds with a frequency of 40 Hz. Find the period of the function that models the sound waves.

O INSTRUMENTS 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.

Modeling O SOUND Humans can hear sounds with a frequency of 40 Hz. Let the amplitude equal 1 unit. Write a sine equation to represent the sound wave y as a function of time t. Then graph the equation.

O INSTRUMENTS The bass tuba can produce sounds with as low a frequency as 50 Hz. Let the amplitude equal 1 unit. Determine the correct sine equation to represent the sound wave y as a function of time t.

12.7 Graphing Trigonometric Functions Day 2: Tangent, Secant, Cosecant, and Cotangent Functions

Example 1 Find the period of. Then graph the function.