Questions on Trigonometric Functions
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This page contains sample problems on trigonometric functions. They
are for Self-assessment and Review. Each
problem (or group of problems) has an "answer button"  which you
can click to look at an answer. Some solutions have a
"further explanation button" 
which you can click to see a more complete, detailed
solution. | What to Do To gain
the most benefit from these problems, Work the
problems on your own. Write down your solutions BEFORE
looking at any answers. Use a graphing calculator as
appropriate. | | If you have difficulties with
this material, please contact your instructor. (See Getting Help in Stage 1.) It
will be very difficult to succeed in Calculus without understanding
trigonometry. |
1. Use the definitions of the six trigonometric
functions and the
Pythagorean Identity given in the Field Guide Lesson to show
that:
- 1 + tan2(x) = sec2(x)
- 1 + cot2(x) = csc2(x)
2. Draw graphs of each of the functions. Give the
period and any
vertical asymptotes. Comment on the amplitudes of
these functions.
- cot (x)
- sec (x)
- csc (x)
3. Give the amplituden and period for
each of the following
functions. Sketch their graphs. Your graphing calculator is helpful
for
checking here.
- g(x) = 3cos 2x
- f(x) = -2.7sin 2(x -
 /4)
- g(x) = sin ((1/2)(x + /3)
- h(x) = 1.5cos (x - 1)
4. The tidal variation in Desolation Sound on the
west coast of Canada
is roughly 4 meters. That is, the difference between water depth at high
tide and at low tide is 4 meters, with successive high tides occurring
12.5 hours apart. Suppose that at Refuge Cove in Desolation Sound, the
depth of water in meters is given by
D(t) = D0 + Acos B(t - t0)
where t is measured in hours from midnight on June 1, 1996.
- What does D0 mean in the context of the
problem?
- What is the value of A?
- What is the value of B?
- Give the physical meaning of t0 for this
problem.
(Adapted by Judy de Szoeke from CALCULUS, (The Harvard Consortium
Text),
Hughes-Hallett, Gleason, et al.))
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