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Section 4.4 Notes

Graphs of SINE and COSINE Functions. Section 4.4 Notes. Graphs of SIN and COS Functions. Stretches – Translations of Sin and Cos Graphs. Can you identify this sinusoid? Graph of sin(x) shifted left by ¼ of period…. OR…. General Form for Sinusoidal Functions. Amplitude = a.

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Section 4.4 Notes

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  1. Graphs of SINE and COSINE Functions Section 4.4 Notes

  2. Graphs of SIN and COS Functions

  3. Stretches – Translations of Sin and Cos Graphs

  4. Can you identify this sinusoid? Graph of sin(x) shifted left by ¼ of period… OR…

  5. General Form for Sinusoidal Functions Amplitude = a Amplitude is half of the total height of the wave. Period is the length of one full cycle of the wave.

  6. which implies…

  7. Setting Your Viewing Window

  8. Tips to get started…

  9. Basic SINE curve starts at ORIGIN, on its way UP

  10. A roller coaster does a 360o loop. The bottom of the loop is 20 off the ground and the loop has a diameter of 100 feet. If it takes the coaster 4 seconds to go around the loop, write a sinusoidal function to determine h(t), the height of the coaster after t seconds. h(t) Height in ft t = time (sec) We could think of the sinusoid we created in two different ways: sine shifted right or the opposite of a cosine curve. We will use the opposite of the cosine curve.

  11. Tarzan is swinging back and forth on a vine. As he swings, he goes back and forth across the river bank below, going alternately over land and water. Jane decides to provide a mathematical model for his horizontal motion and starts her stopwatch. Let t be the number of seconds that the stopwatch reads and y be the number of meters that Tarzan is from the river bank. Assume that y varies sinusoidally with t, and that y is positive when Tarzan is over the water and negative when he is over the land. • Jane finds that when t = 2, Tarzan is at one end of his swing, where y = -23. She finds that when t = 5, he reaches the other end of his swing and y = 17. • Sketch a graph of the sinusoidal function. • Write an equation expressing Tarzan’s distance from the river bank in terms of t. • Predict y when t = 2.8 and t = 15 • Where was Tarzan when Jane started the stopwatch? • When t = 0. • Find the least positive value of t for which Tarzan is directly over the riverbank. • When y = 0.

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