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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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Graphs of SINE and COSINE Functions Section 4.4 Notes
Can you identify this sinusoid? Graph of sin(x) shifted left by ¼ of period… OR…
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.
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.
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.