Last modified 27 June 2003 by jdavis@math.wisc.edu

Exam 1 Review

I might be adding more stuff to this page up until the exam, so you might want to check back occasionally.

Here are some general things to keep in mind:

• No calculators are allowed.
• Exact answers are always required, except where I explicitly ask for a decimal approximation.
• Try to simplify your answers as much as possible. For example:
  • "one half of the square root of 8" should be simplified to "the square root of 2".
  • "cos x tan x" should be simplified to "sin x".
  • "sin(pi/6)" should be simplified to "1/2", but "sin(pi/37)" can't be simplified.
• Angles are almost always expressed in radians. Remember, sin(30) means "sine of 30 radians", not "degrees". If you want to write "degrees", then you need to use the degree symbol (the little, raised circle).

• Conversion among radians, degrees, and revolutions. The 16 common angles, and the values of sin and cos there.
• The definitions of all six trig functions, in terms of sin and cos, and in terms of a point on the terminal ray of the angle.
• The Pythagorean theorem, the sin²x + cos²x = 1 identity, and how to solve right triangles.
• Story problems involving right triangles, arc length, angular vs. linear speed, etc.
• The opposite angle identities: sin(-x) = -sin(x) and cos(-x) = cos(x).
• Using algebra and trig identities to simplify formulae or prove equalities. Practice!
• The graphs of sin, cos, and tan. How to compress and expand graphs. How to shift graphs up/down and left/right. Periods.

This test will NOT make significant use of the inverse trig functions sin^-1, etc. They are dangerous to use, until we have studied them in detail.

Although you will need to be able to convert angles among radians, degrees, and revolutions, you will NOT need to do unit conversions such as feet/sec vs. mi/hour.

The best way to study for the test is to do as many book problems as you can. Try to make up some of your own problems. Study with others.