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FST Section 4.10.  Looking at sin, cos, and tan from the unit circle  nitcircle.html

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Presentation on theme: "FST Section 4.10.  Looking at sin, cos, and tan from the unit circle  nitcircle.html"— Presentation transcript:

1 FST Section 4.10

2  Looking at sin, cos, and tan from the unit circle  http://www.analyzemath.com/unitcircle/u nitcircle.html http://www.analyzemath.com/unitcircle/u nitcircle.html

3  Wind Turbines  Practice Problems

4  Graph/describe each of the following: a) f(x) = cos (x + π/4) – 1 b) f(x) = 2 sin (3x + π) + 2

5  P. 292 Activity (with a partner)  CALCULATOR!

6 Date1/152/153/154/155/156/15 Day154674105135166 Hours of Daylight 8.8810.311.8513.6215.115.95 Date7/158/159/1510/1511/1512/15 Day196227258288319349 Hours of Daylight 15.5814.2712.610.929.338.48

7  Slinky

8  When weight is suspended from a spring attached to a rod, it will remain in the equilibrium position, unless disturbed.  If the weight is pulled a small distance, it will oscillate indefinitely about the equilibrium position (assuming no friction).  For example, at t = 0, the weight is pulled 3 cm. After 1 sec, it is back to equilibrium. After 2 sec, it is 3 cm above equilibrium… etc.  Find an equation of a sine curve to fit these data.

9  Simple harmonic motion  All materials have a natural harmonic frequency  This video also includes an example of an oscillating weight on a spring  Videos: http://www.youtube.com/watch?v=eeYRkW8 V7Vg&feature=fvw http://www.youtube.com/watch?v=eeYRkW8 V7Vg&feature=fvw

10  A satellite is deployed from a space shuttle into an orbit which goes alternately north and south of the equator.  Suppose the satellite is y kilometers north of the equator at x minutes. (y < 0 for south)  It reaches 4500 km, its farthest point north of the equator, 15 mins after launch. Half an orbit later, it is 4500 km south of the equator.  One complete orbit takes 2 hours. 1) Find an equation using cosine to model the distance of the satellite from the equator. 2) How far away from the equator is the satellite 1 hour after launch?

11  The motion of a piston in a car’s engine follows a sine curve.  See the following example: http://www.intmath.com/Trigonometric- graphs/2_Graphs-sine-cosine-period.php

12  Electromagnetic waves – The interaction between electrically charged particles: includes light waves, radiation, radio waves, etc. Videos: http://www.youtube.com/watch?v=xZ6XUk7QLbU& p=9B166389CACF63CA&index=41&playnext=2 https://www.youtube.com/watch?v=m4t7gTmBK3g

13  Pendulum swinging  Video: http://www.youtube.com/watch?v=X- OCz9lIiY4&feature=related http://www.youtube.com/watch?v=X- OCz9lIiY4&feature=related

14  Guitar string video  Video: https://www.youtube.com/watch?v=TKF 6nFzpHBU&feature=player_embedded https://www.youtube.com/watch?v=TKF 6nFzpHBU&feature=player_embedded

15  4-10 Worksheet 2.  Page 297 - 298 # 8, 9a-d, 10, 13, 14, 16 MonthJanFebMayJulAugNov 303564807843


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