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Exercise 1:
The Pythagorean Identities are among the most
important you will learn in your studies of trigonometry. To learn more about the history
of Pythagorus, go to Pythagoras
of Samos. Pythagorus may have had a good handle on geometry and trigonometry, but what
were his ideas about astronomy? |
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Exercise 2:
In section 6-2, you saw how trigonometry is
used to describe light refracting through a plate glass window. To learn more about
trigonometry is used to describe light refraction through other substances, like water, go
to The Mystery of Refraction.
Who invented the law of refraction that is discussed on this site? What is the index of
refraction of diamond? Now, use the equation,sin(i)= 1/n (discussed on the site)
to find the angle of incidence at
which ray of light passing from diamond to air is refracted and moves parallel to the
surface.
(answer)
(Did you see how the cover art of
Pink Floyd's Dark Side of the Moon was created!) |
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Exercise 3:
An instrument called a sextant is mentioned in
some of your text exercises. Go to Sextant to see a great
picture of a and find out how this instrument works. Now, go to Celestaire and find out what sextants are
used for, other than surveying. If you want to really get into it, go check out this site! |
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Exercise 4:
Ok, what is all this trigonometry stuff good
for? And while you're at it, what good are logarithms?! You like music, don't you? Go to Karen's Damping Functions at
Coolmath.com to find out how math is used in music. Be sure to read all four pages of the
lesson and, then, answer the boxed questions at the end. |
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Exercise 5:
In section 6-4, you learned how musicians use
trigonometry and beat frequencies to tune their instruments. Let's look at the guitar, for
example. The entire guitar can be tuned (so it sounds just right) if it is assumed that
the top string is "in tune". When one string of a guitar is plucked, the sound
waves produced are a combination of sine waves. (As you saw in exercise 4.) But, when a
musician plucks a string while just touching a finger to the string, lightly pressing the
string so it does not touch the fret, pure sine wave is produced. These tones are called
harmonics and sound like a glass being stuck. When a harmonic on each of two neighboring
strings is plucked (at certain frets), the two tones should be exactly the same, if the
strings are in tune with each other. To hear how this sounds, check out Beats and play with the applet to get the two tones to match up. |
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Exercise 6:
To get some practical experience in simple
harmonic motion, go to The Pendulum. This
applet will allow you to swing a pendulum while watching the periods. If you want to learn
more about the physics involved, go to Oscillations. |
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