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Exploring Trigonometric Functions: Amplitude, Period, and Graphing

Learn to find amplitudes and periods, graph sine and cosine functions, discover x-intercepts, and apply trigonometry in sound wave modeling and musical instruments. Advance to tangent, secant, cosecant, and cotangent functions.

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Exploring Trigonometric Functions: Amplitude, Period, and Graphing

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  1. 12.7 Graphing Trigonometric Functions Day 1: Sine and Cosine

  2. Finding Amplitude and Period Example 1a • Find the amplitude and period of

  3. Example 1b • Find the amplitude and period of

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

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

  6. Graphing Trigonometric Functions • Graph the function y = 2sin . • First, find amplitude and period • Next, find x-intercepts • Graph

  7. Graphing Trigonometric Functions- You try • Graph the function y = 4sin . • First, find amplitude and period • Next, find x-intercepts • Graph

  8. Applications

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

  10. 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.

  11. Modeling • 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.

  12. 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.

  13. 12.7 Graphing Trigonometric Functions Day 2: Tangent, Secant, Cosecant, and Cotangent Functions

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

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