Precalculus Verifying identities

[choirfarm]

Can you point me into the direction of extra help with verifying identities in chapter 5 of Chalkdust. Oldest made a C on the test. He missed 5 out of 10 on that section. His only other error was a careless one. But he doesn't get the concept at all. He is also confused about when he puts the answer in the theta sign or in the x sign. He's not sure why they do each one. I'm not sure how to do all of the symbols on this board. Here is a problems that he put a question mark on ( VERY rare for this child..he NEVER does that)

 

csc alpha sign + sec alpha sign = cot alpha sign + tan alpha sign

sin alpha sign + cos alpha sign

 

 

Thanks

Christine

[Teachin'Mine]

The theta sign just means angle - so it's read as co-secant angle plus ...

 

Not sure but Brightstorm or Khan should have some good videos to help.

 

Dd says that whether the theta sign is used or an x, they would both be worked the same. Just continue to use whatever they use. Kwim?

Edited November 23, 2011 by Teachin'Mine
removed useless link

[kiana]

Can you point me into the direction of extra help with verifying identities in chapter 5 of Chalkdust. Oldest made a C on the test. He missed 5 out of 10 on that section. His only other error was a careless one. But he doesn't get the concept at all. He is also confused about when he puts the answer in the theta sign or in the x sign. He's not sure why they do each one. I'm not sure how to do all of the symbols on this board. Here is a problems that he put a question mark on ( VERY rare for this child..he NEVER does that)

 

csc alpha sign + sec alpha sign = cot alpha sign + tan alpha sign

sin alpha sign + cos alpha sign

 

 

Thanks

Christine

 

1) I'd go to Khan. Sometimes you just need to see a lot of examples.

 

2) They use many different variables for angles. It's just like ... in algebra, you might be told to solve an equation in x, then an equation in y, then an equation in t ... just continue using whichever one they started with.

 

3) Just about every precalc student I've ever had has had trouble with this. It's a different way of thinking.

[MyThreeSons]

1) I'd go to Khan. Sometimes you just need to see a lot of examples.

 

 

I'd recommend not just seeing lots of examples, but actually working thru each one, step by step. For many of us, there's something about writing it down that helps to cement the concepts. He may have to start out by copying example problems, making sure he understands the process.

 

He may have to wrestle with figuring out how they got from one step to the next. It really is just like algebra, going from one step to the next, except that you're usually doing more substitution than arithmetic operations. He should have a list of the trig identities handy that he can refer to. It often helps to look at each term or combination of terms in the problem and see whether there is another way to write it; whenever he sees csc theta, for instance, there's a really good chance that it's going to help to substitute 1/sin theta.

 

HTH

[regentrude]

He just needs to understand that the name of the variable does not matter at all. Whether the angle is called alpha or theta or x or something completely crazy, it is the same identity. So, he should simply use the symbol that is used in the problem - alpha in your example.

 

He should recall that, when he solved linear equation in algebra 1, he would do exactly the same whether the variable was called x or a or b. Same here.

 

I second the recommendation for Khan, and for writing out the problems himself step by step. In my experience, just seeing somebody work a problem can be useless because it looks easy and logical - the student must work through each problem himself to get any benefit.

[choirfarm]

Well, he looked at Khan yesterday http://www.khanacademy.org/video/trigonometric-identities?playlist=Trigonometry but the identity part he already knew and it wasn't what he had problems with. I'm thinking maybe the next videos on proofs is where he had trouble. http://www.khanacademy.org/video/proof--sin-a-b------cos-a--sin-b-----sin-a--cos-b?playlist=Trigonometry

 

I'll have him watch it, though technically today isn't a school day. He is taking an AP Chemistry exam today, however. I can probably talk him into it since it is math and not writing. :) He might find it fun to figure out.

[Caroline]

Well, he looked at Khan yesterday http://www.khanacademy.org/video/trigonometric-identities?playlist=Trigonometry but the identity part he already knew and it wasn't what he had problems with. I'm thinking maybe the next videos on proofs is where he had trouble. http://www.khanacademy.org/video/proof--sin-a-b------cos-a--sin-b-----sin-a--cos-b?playlist=Trigonometry

 

I'll have him watch it, though technically today isn't a school day. He is taking an AP Chemistry exam today, however. I can probably talk him into it since it is math and not writing. :) He might find it fun to figure out.

 

Yes, verifying indentities is a proof technique, so the second video is probably what you want.

 

I know that technically this method isn't always the fastest or most elegant way to do these problems, but I always start by changing all of the most complicated side to sines and cosines. I just work better in sines and cosines.

[kiana]

Yes, verifying indentities is a proof technique, so the second video is probably what you want.

 

I know that technically this method isn't always the fastest or most elegant way to do these problems, but I always start by changing all of the most complicated side to sines and cosines. I just work better in sines and cosines.

 

Yes, this is a good general rule. Pick the ugliest side, change everything to sines and cosines and apply algebra to simplify.