SURVIVING A (TRIG) IDENTITY CRISIS
"If you were stuck on a desert island,
which trig identities would you want to have with you?"
Let's start with some poetry by high school trig students:
one by Elizabeth Palmieri
one by Erin Stanley
Good books, etc. for reference:
- Most (if not all) precalculus or calculus textbooks have a trigonometry appendix
(e.g., page A22ff of Stewart, 2nd ed.)
- CRC Standard Math Tables
(e.g., 27th edition, page 137ff)
- A TI-89 or TI-92, which do trig manipulation with tExpand and tCollect
- Any other graphing calculator, for verifying trig identities graphically or numerically
Resources on the Web
A fundamental set of relationships and identities
- SOHCAHTOA (right-triangle trig)
Note: There is no substitute for remembering the basic definitions!
- ... leads to Pythagorean identities and co-function relationships
- Extending trig functions to the unit circle
- ... leads to periodicity and reflection relationships [e.g., sin(px)=sin x]
- Sine and cosine double angle identities (sin 2x = 2 sin x cos x; cos 2x=cos2x sin2x)
- ... leads to angle sum/difference formulas,
and also to the half-angle formulas for sine and cosine
- Others ...?
CMJ problem 709
Basically, this problem asked for solutions to the equations
where q and x are both rational ....
(a) p/4 = arctan(q) + arctan(x)|
(b) p/4 = arctan(q) + 2arctan(x)