MATH 103
Recommended problems from Exercise Sets 4.2, 4.3, 4.4, etc.
(in Faires & DeFranza)
Exercise Set 4.2:
- Do a couple from the group 1-8.
(Conversion from degree to radian measure; page 188.)
- Do a couple from the group 9-14.
(Conversion from radian to degree measure; page 188.)
- Do a couple from the group 15-20. Two angles "coincide" if,
when both are in "standard position", their terminal sides
are the same. This corresponds to their measures differing
by a multiple of 2π radians or, equivalently, a multiple of
360 degrees.
- Do a couple from among 25-28.
The keys to remember are that P(t) and P(t+π) have the same
coordinates, except that their signs are flipped, and
P(t) and P(-t) have the same coordinates, except that one of
the two signs is flipped.
(Which one depends upon in which quadrant P(t) lies.)
- Do a couple from among 29-34.
The key to remember is that (see page 191)
s = rθ (or θ = s/r), where r is radius,
s is arc length, and θ is angle measure (in radians).
- Do a couple from among 35-40.
The key to remember is that (see page 192)
A = r2θ / 2, where A is area of a circular sector,
r is radius, and θ is angle measure (in radians).
Exercise Set 4.3:
- Do a couple from the group 1-6.
The key is to use the rules (see Figure 10 on page 201) for
calculating a reference number/angle.
- Do a few from the group 7-24.
The keys are calculating reference numbers/angles and making use
of known values of sine and cosine in the interval [0,π/2].
- Do a couple from the group 39-46.
The keys are as immediately above, but, in addition, you need to be
able to calculate, for a given number/angle t in the interval
[0,π/2], for which other numbers (in some interval) t
serves as a reference number/angle.
- Do 51.
- Try a couple from among 52-55. These are more difficult problems.
The key in 52-54 is to use factoring. In 55, take the given equation
and the Pythagorean Identity and solve them "simultaneously".
Exercise Set 4.4:
- Do a few from the group 1-4. Recall that, if f is a
periodic function with period T, then g(x) = f(Bx)
has period T/B. As special cases, the period of
both sin Bx and cos Bx is 2π/B.
- Do a few from the group 5-18.
- Do a few from the group 19-22.
- Do 23-24.
- Do at least one of 25-26.
- Do at least one of 35-36.
For example, in 35a you want to find the smallest positive value
of t for which 3t - π/4 is a multiple of
π (because it is at multiples of π that sin has value
zero). Similarly, because sin x attains its maximum value
when x is of the form 2nπ+π/2
(i.e., when x exceeds a multiple of 2π by π/2),
to answer 35b you want to find the smallest positive value of t
for which 3t - π/4 exceeds by π/2 a multiple of 2π.
Exercise Set 4.5:
- Do a few from the group 1-6.
- Fill in the first two rows of the tables in 7 and 8.
The rest of the entries can be calculated directly from
the definitions of the other four trigonometric functions
in terms of sin and cos.
- Do a few from the group 9-16.
- Do a few from the group 29-36.
- Do 43.
Exercise Set 4.6:
Exercise Set 4.7: