Here's a rough idea of what I think is important for the first midterm.
You can also keep an eye out for a practice midterm, which will probably
be posted on Monday.
- Angles. Positive and negative angles. Conversion between radians and
degrees.
- Definitions of trig functions. Given a point (x,y) on a circle of
radius r which corresponds to an angle t, you should be able to give me
the value of the trig functions. [For example, sin(t)=y/r.] In class we
usually used a circle of radius r=1, which made the definitions easier,
but you may or may not run across a circle with a different radius on the
test.
- Exact values of the trig functions. You should be able to give me exact
values (no decimals) of the trig functions for all of our "nice" angles:
multiples of 30 degrees and multiples of 45 degrees. You can find all of
these by drawing a 30-60-90 or 45-45-90 triangle within a cirlce and using
the definitions.
- properties of the trig functions: even/odd, domain/range, min/max, where
the zeros are, etc.
- Graphs of the trig functions. You should be able to work with the
"general" equations such as y=A*sin(wx) or y=A*sin(wx-p). Same for
cosine. You should be able to graph tan(x) and apply some basic
transformations to it. Given a graph of (for example) cot(x) you should
be able to graph something like 2*cot(x-1).
- basic trig identities, such as those in section 5.4.
- Inverse sine and cosine functions. (We'll continue talking about these
on Monday)
More details this week in class --
Jon