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Warm up

Find sin (-5 ) Find the values of ϴ for which cos ϴ =1 is true. Graph the function y = sin x for the interval. Warm up. Objective: To find the amplitude and period of sine and cosine functions. To write equations of sine and cosine functions given the amplitude and period.

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Warm up

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  1. Find sin (-5) • Find the values of ϴ for which cosϴ=1 is true. • Graph the function y = sin x for the interval Warm up

  2. Objective: To find the amplitude and period of sine and cosine functions. To write equations of sine and cosine functions given the amplitude and period. Lesson 6-4 Amplitude and Period of Sine and Cosine Functions

  3. In the last lesson we learned that the period was the domain over which the graph repeats. • The period of and is where k > 0. Period

  4. For the equation y= A sin the maximum absolute value of the graph is 1. • This is the amplitude. Amplitude

  5. Amplitude • It can also be described as the absolute value of half the difference of the maximum and minimum values of the function. • Example: y = 4sinθ The amplitude is 4… The maximum is 4 and the minimum is -4. So (4 - -4)/2 = 4

  6. Frequency is the number of cycles per unit of time. • Period and Frequency are reciprocals of each other. • Frequency is measured in units called hertz. • 1 hertz = 1 cycle per second Frequency

  7. State the amplitude for the function • State the amplitude and period for the function then graph the function Examples

  8. Write an equation of the sine function with amplitude 2 and period • Start with • So

  9. A pendulum swings a total distance of 0.30 meter. The center point is zero. It completes a cycle every 2 seconds. • Assuming that the pendulum is at the center point and heading right at t=0, find an equation for the motion of the pendulum. Practice

  10. The Sears Building in Chicago sways back and forth at a vibration frequency of about 0.1 Hz. On average, it sways 6 inches from true center. Write an equation of the sine function that represents this behavior. Practice

  11. interactive sine graph

  12. Interactive Mathematics. N.p., n.d. Web. 27 Oct. 2013. <http://www.intmath.com/ trigonometric-graphs/1-graphs-sine-cosine-amplitude.php>. • Handbook for Acoustic Ecology. Cambridge Publishing, 1999. Web. 28 Oct. 2013. <http://www.sfu.ca/ sonic-studio/handbook/Sine_Wave.html>. Sources

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