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Exercise 1:
Getting familiar with the Unit Circle will
greatly help your ability to evaluate sine values for given angles. Visit the Sine Box and enter in at
least 15 angle values ranging from -360 degrees to 360 degrees. |
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Exercise 2:
One of the most important things that you will
be using trigonometry for in calculus is to solve equations for some unknown angle. Now
that you've practiced with exercise 1, try your luck at Sin t = a. How many
should you try? Well, how good to you want to get? Why don't you shoot for getting at
least 7 out of every 10 tries correct. (And, if you're just off by 5 degrees, that's still
pretty good!) |
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Exercise 3:
From exercises 1 and 2, you should have sine
and the Unit Circle down to a science. To make the connection between the Unit Circle and
the graph of y = sin(x), visit Graph of y = sin x. To
get the best results, do NOT hit the "draw" button as they tell you -- Click on
the "+" button to draw the graph a little at a time. |
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Exercise 4:
This exercise is just like exercise 1, except
we'll be investigating cosine values. Visit the Cosine Box and enter in at
least 15 angle values ranging from -360 degrees to 360 degrees. |
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Exercise 5:
This exercise will be like exercise 2 for
cosine. Now that you've practiced with exercise 4, try your luck at Cos t = a. Once again,
shoot for getting 7 out of every 10 tries correct! |
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Exercise 6:
From exercises 4 and 5, you should know you
cosine values and the Unit Circle like the back of your hand. To make the connection
between the Unit Circle and the graph of y = cos(x), visit Graph of y = cos x.
Once again, to get the best results, do NOT hit the "draw" button as they tell
you -- Click on the "+" button to draw the graph. |
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Exercise 7:
For this exercise, you have two main goals.
The first is to get accustomed with the ideas of wavelength, amplitude and phase when
graphing sine (and cosine, which is just sine with a shift). Now that you've seen the
standard equation, y = A*sin(Bx+C), and tried your hand at some graphing, Interference of
Sinusoidal Waveforms will allow you to adjust these values and immediately see the
effects. Your second goal is to see what happens when two sine waves are added together!
(You did this back in section 3-5.) As you'll see in the next exercises, sounds are
combinations of sine waves! |
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Exercise 8:
Did you know that a man named Eratosthenes,
Director of the great library of Alexandria in Egypt, measured the radius of the Earth in
about 200BC with nothing but a stick and some trigonometry? Pretty creative, don't you
think? Go to Measuring
the Earth, Moon and Sun and read all about it. Write a one page report describing the
math process that was used to make one of these huge measurements described on this site. |
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Exercise 9:
To see yet another application of
trigonometry, go to Surveying the
Uses of Trigonometry. Check their math to make sure it's accurate and then do similar
calculations assuming piranha infested waters, an angle of 50 degrees and a length of 250
ft.
(answer) |
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Exercise 10:
To see the graphs of some musical notes, go to
Play a Piano. Warning:
Do NOT hit the "play" button for Jingle Bells -- It may not stop! When you hear
the first note play, the applet is ready to go. Try playing some individual notes on the
keyboard. What do you notice about the graphs and frequencies of the high notes as
compared to the low notes?
(answer) |
