6.4 Be able to use the Law of Sines (Box, p.506) to solve triangles
when you know one side and two angles: ASA (*Example 1*,
*Exercises 2, 3*), or
SAA (*Example 2*, *Exercises 1, 6*).
In these two cases all three of the angles
in the triangle are known. Understand the ambiguity when you apply the
Law of Sines to SSA problems (*Examples 3, 4, 5*): if you know
sinθ there are in general **two** possible θs between
0° and 180°, and **sometimes** there are two different
solutions to the problem (*Exercises 15, 16, 32*).
*The* sin^{-1} *key on your
calculator only gives you the angle between* 0° *and*
90° *with that sine*. Understand this fact of life.

6.4 Be able to use the Law of Cosines (Box, p.513) to solve triangles
when you know all three sides (*Example 2, Exercises 5, 6, 8*)
or two sides and the angle between them: SAS (*Example 1, Exercises
1, 2, 3, 27*).

5.1 Be comfortable with the unit circle. The circumference is
2π = 6.28.. Be able to estimate locations of angles from their
radian measure (*Exercises 43-46*). Be comfortable in converting
radians to degrees, and degrees to radians.

5.2 In your revision, concentrate on the functions `sin`,
`cos`, and `tan`, and the fundamental identities
`tan = sin/cos` and `sin ^{2}+cos^{2}=1`.
Always remember the definitions of

5.3 `sin` and `cos` have period `2 pi`: they
repeat exactly every `2 pi` units. The function
`y=a sin k(x-b)` can be derived from `y=sin(x)`
by three of our elementary changes: `sin(x) -> sin(kx)
-> sin(k[x-b]) -> a sin(k[x-b])`, corresponding to a
compression of the graph by a factor of `k` (so the
new period is `2 pi/k`), a shift to the right by `b` units,
and a vertical scaling by `a`. The absolute value
`|a|` is the amplitude, and `b` is the phase shift.
If you are given the function in the form `sin(kx-d)`
be sure to rewrite it as `sin(k[x-d/k])` before evaluating
the phase shift and using it to sketch the graph. *Exercises 21-34.*

5.4 Here concentrate on the graph of `tan`. The function has
period `pi`. Be able to graph functions of the form
`a tan([k(x-b)]` by the same methods as before. *Examples 1,2,
Exercises 1,4,19,31*.

7.1 The best method for dealing with trigonometric
identities is to 1) rewrite everything in terms of
`sin` and `cos` and 2) try to rearrange
terms so as to be able to apply `sin ^{2}+cos^{2}=1.`
Other algebraic identities you may need are

7.2 Do not try to memorize the addition formulas for
`sin` and `cos`. If you need them on the test they
will be written out there. Be able to *use* the formulas
(*Examples 1,2,3, Exercises 1-8, 11, 12, 21-24*

7.4 Understand the three basic inverse trigonometric functions
`sin ^{-1}`,

Calculus 2.1 Understand the relation between the *tangent* (line)
to the curve `y=f(x)` at the point `(a,f(a))` and
a *secant* (line) passing through the points `(a,f(a))`
and `(a+h,f(a+h))` for `h` nonzero. We can calculate
the slope of the secant by the "rise over run" method. If the curve
is smooth (Fig. 3 p.96) the secants will approximate the tangent
as `h` becomes small. In case x is time and f(x) is position,
understand that the slope of the secant is the *average velocity*
between `a` and `a+h`. *Exercises 4, 5*.

Calculus 2.3 and 2.6 Be able to calculate limits of the type encountered
in tangent and velocity problems, in case the function `f(x)`
is a polynomial of degree two.
*Example 3 p.113, Example 5 p.114*.
*Example 1 p.143, Example 3 p.145*. Be able to use these limits
to calculate the equation of the tangent line by the point-slope
method. *Exercises 15, 16ab, 18, 20, 21 p.148-149*

December 6, 2003