
Questions on Trigonometric Functions
What's On
This Page
This page contains sample problems on trigonometric functions. They
are for Selfassessment 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 + tan^{2}(x) = sec^{2}(x)
 1 + cot^{2}(x) = csc^{2}(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) = D_{0} + Acos B(t  t_{0})
where t is measured in hours from midnight on June 1, 1996.
 What does D_{0} mean in the context of the
problem?
 What is the value of A?
 What is the value of B?
 Give the physical meaning of t_{0} for this
problem.
(Adapted by Judy de Szoeke from CALCULUS, (The Harvard Consortium
Text),
HughesHallett, Gleason, et al.))
