posted
I'm taking a precalc course and so far I've done well but this material is sort of headache inducing as you aren't even solving an equation but merely "veryfing it" so one side--through conversion using various formulas--resembles the other.
posted
Convert all the trig functions to the ratios they represent. That always made it easier for me.
Posts: 26071 | Registered: Oct 2003
| IP: Logged |
If it gets uglier for more than two consecutive steps, you're probably doing something wrong.
When all else fails, turn everything into sine and cosine. (i.e., no tan, cot, csc, or sec)
When all else really fails, go ahead and break the rules: work on both sides. You're not supposed to, so do it on another piece of paper. Once you find the key, you can go back and fake the work.
quote:what are good methods for verifying trig identities?
I usually put them in cages with other trigs and see what happens. In a couple of weeks you'll be able to tell who's who pretty easily.
Posts: 22497 | Registered: Sep 2000
| IP: Logged |
posted
No, or at least it didn't at my college. But then there's also epsilon-delta proofs, and other kinds of headaches...
Posts: 283 | Registered: Jul 2006
| IP: Logged |
posted
Verifying trig identities? Not so much per se, although it could come up in the form of proofs of other stuff. Depends on how proof-happy your calc teacher is. However, to be good at verifying them, you have to know them well, and that will certainly come up again, when you're trying to differentiate or integrate trigonometric ratios. Also, if you plan on taking the AP exam, memorize your trig identities! If your precalc teacher lets you use a reference sheet or a notecard--as I have wrongfully done for years--s/he is not doing you any favors, as you will not be allowed any sort of reference on the AP calc test.
Posts: 13680 | Registered: Mar 2002
| IP: Logged |
posted
I always loved trig and trig identities. And I have to completely agree with Icarus - memorize those crazy suckers!
Posts: 3932 | Registered: Sep 1999
| IP: Logged |
posted
There is also the fun solution of converting everything to exponentials, simplifing and converting back. Although that may be beyond the scope of your class.
Posts: 1621 | Registered: Oct 2001
| IP: Logged |
Funny, I tried memorizing trig identities three times through three courses, and it never made sense. It worked for a given test, but didn't stick with me.
Then I did exactly what you said above, and converted the identities into the ratios they represented. It was slower than using memorized "facts," but the meaning has not left me since. I would say your original advice is the best one here.
Posts: 3735 | Registered: Mar 2002
| IP: Logged |
Hey, if its good enough for your local polling place, it should be good enough for class.
Although, there is always the problem of Trig Identity Theft. One forged cosine and who knows what chaos may follow.
Posts: 11895 | Registered: Apr 2002
| IP: Logged |
posted
Yeah, that's a problem. A friend of mine had his fiancee cosine on a loan, and then they broke up. She was responsible for his debt under the law of cosines.
Posts: 3735 | Registered: Mar 2002
| IP: Logged |
posted
I had problems with this, because every time I'd try to verify trigonometric Identities I would end up roughing them up a little to get 'em to talk, and invariably they would give me false information. On my Precal midterm I held this fresh little secant out the window upside down, and he shouted "Ok, ok, I'm a Cosine." (The lying little jerk). So I'm like "Hey, you were a Secant a couple seconds ago, and now that you're inversed you're trying to tell me you're a Cosine, nice try." Long story short I failed the test.
Well… not really.
Posts: 959 | Registered: Oct 2005
| IP: Logged |
posted
Yeah, he was a tangent, that's why she fell for him. Tall dark and handsome. She was pretty acute too.
Posts: 3735 | Registered: Mar 2002
| IP: Logged |
Printer-friendly view of this topic
