5.2 – Verifying Identities
Dec 7th, 2010 by corricelli
Hello!
Please use this section to post questions/concerns/reflections on Chapter 5, Section 2.
Happy Blogging,
Mrs. Corricelli
25 Responses to “5.2 – Verifying Identities”
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For number 53 its says that you have to graph each side of (1 – cot^2x)(cos^2x) = cot^2x. I understand that but how do you plug in a trig function with a power that is not attached to the x into a graphing calculator??
is cot^2x the same as cotx^2 ?
Hey Brian,
Yes! cot^2x is the same as (cotx)^2.
However, note that it IS NOT the same as cotx^2 b/c this really means that only the x is squared. cotx^2 = cot(x^2), b/c of order of operations. This is why this notation was invented.
(In words, “cotangent squared of x”) This, admittedly, looks strange.
Thanks,
Mrs. Corricelli
I’m sort of confused about what you do to verify an equation that is not an identity, like number 55 i think it was. I just ended up getting it close to being verified, but obviously not an identity
I think because when you graph the two equations for #55, you see they are not the same, so you know you can’t show that they equal eachother. I think what your supposed to do is show, or verify, that they are unequal.
Hey guys, I’m just wondering how you’re getting into your trig identity projects, because i made an equation just by choosing some of the trigonometric functions and trying to see what they equal, maybe not the best method.. Plus I end up with a squared trig function plus a normal one so i cant really use any of the sin^2 + cos^2 stuff right?
Becca, what I am doing is starting with a simple combination of trig functions, such as cosx + sinx for example. Then using what you know change things around while keeping the entire thing equal. Then at the end you can say that this huge crazy thing equals cosx + sinX
Mrs Corricelli,
On number 47 on the weekends homework, I was wondering how to change around inverse sine, besides turning it into arcsin which doesn’t really do anything.
On page 386 for tonight’s homework how do you do number 65.
Hi Becca,
You pretty much combine identities; maybe yours can eventually simplify to sine squared + cosine squared.
I think it’s easier to combine and see what you get than having an end goal and figuring out which trig functions will get you there.
Becca,
I agree with Mariah. This is a creative assignment. Start anywhere. End up anywhere. You cannot really be wrong UNLESS you do not use three trig functions to start, do something mathematically wrong, and/or do not follow directions given to you on the Identity Assignment paper.
The question is, “What is Becca’s identity?” Hmmm?
Good luck to Teams 2 and 7 on finding your identities!
I am really looking forward to seeing your work.
Sincerely,
Mrs. Corricelli
hey i’m also kind of stuck on 47 as is joe.
do you think graphing would help?
i don’t understand how the trig functions and lead to an expression with only the variable x….
also the example on calcchat doesn’t make sense. its not even the right question….
jk calc chat hss it…. but im still really confused.
has**
ok so scrach all of that. this is kind of funny im having a convo with myself haha.
joe- use the substitutions we did in the last chapter. let u= arcsin and continue.
DRAW A TRIANGLE
Joe and Rachel,
I agree with Rachel’s emphasis on DRAWING. See Rachel – art is SO useful!
Happy art aka math,
Mrs. Corricelli
I have the same question as Srinath.
For number 65 I looked at calc chat, but i dont understand how Sin^2(65°) can = cos^2(90°-65°)
Sabrina (and Srinath)
Note: These are COFUNCTIONS. So cos(complement of x) = sin(x). So cos(90-x)=sinx.
This is a FUNdamental identity.
Take care,
Mrs. Corricelli
Hey guys,
I have a quick clarifying question…
is tan^2x equal to sin^2x/cos^2x or sin^2x/cos x?
Haley,
What Rachel said.
Note that you have the tools now to verify this identity… When in doubt, employ them! They are pretty POWERful.
(tanx)^2 = (sinx/cosx)^2 = (sinx/cosx)*(sinx/cosx)=[(sinx)^2]/[(cosx)^2].
Happy blogging,
Mrs. Corricelli
Haley- cos is squared too
For the Homework this weekend are we suppost to show the exceptions even though the book isn’t asking for it?
Colleen,
Yes – show the exceptions. That is what you need to be prepared to handle on the quiz, too!
Take care,
Mrs. Corricelli
Ok, Small problem, is it ok to say that your theta is unequal to 0, pi/2,pi, and 3pi/2 , all of them plus 2pin where n is in the set of integers
also, if secx is unequal to 0 and cotan x is unequal to 0, are my restrictions really cos x is unequal to 0 and sin x is unequal to 0 (thats how i got the restrictions above)
Becca, I think that’d be okay to say that theta is unequal to 2(pi)(n) with n as the set of integers
And I also think that is correct because it’s making sure that in the denominator (which would be sin x and cos x) isn’t zero.
Beckeezy,
I think that work is right (just from looking at it though) but your not restricting everything if that’s what your thinking?
do you have two of those restrictions for sine and two for cosine?
If you do, you can condense them:
sin x cannot equal: pi + pi n …where n is in the set of integers
and
cos x cannot equal: pi/2 + pi n …where n is in the set of integers
does that help at all?..