|
|
|
|
New Member
|
|
Oct 6, 2009, 12:16 PM
|
|
How do you verify Trig. Identities?
I do not understand how to verify Trig. Identities and I have an upcoming test soon. For example, how do I solve this:
Sin^2Theta+Tan^2Theta+Cos^2Theta=Sec^2Theta
This was a problem out of the book, but it's not part of any homework. I didn't really know how to make a problem for this up. I have a list of formulas my teacher gave me, but which ones to use are confusing. Help please?
|
|
|
Ultra Member
|
|
Oct 6, 2009, 01:09 PM
|
|
|
|
|
New Member
|
|
Oct 6, 2009, 01:29 PM
|
|
I'm not sure I understand how to set that up.
Like this?
Cos(pi/2-Theta)+SinTheta/CosTheta+Sin(pi/2-Theta)
Eh, I really don't think I set it up right? I'm using the formulas my teacher gave us, by the way.
|
|
|
New Member
|
|
Oct 6, 2009, 01:31 PM
|
|
Also, what do I do with the exponents? (by the way, thanks for helping me I really appreciate it!)
|
|
|
Ultra Member
|
|
Oct 6, 2009, 07:43 PM
|
|
rearrange to make it clearer
using the identities I gave above, you get:
and therefore
QED
|
|
|
Uber Member
|
|
Oct 6, 2009, 11:27 PM
|
|
Could you mention all the formulae your teacher gave you? Because for identities, I have quite a small lot, for those which do not require double angles... actually 9. And with them, I can prove your identity, faster than what Perito suggested, which I am not saying is bad. Any method you use is good, provided you know what you're doing.
|
|
|
New Member
|
|
Oct 7, 2009, 08:50 AM
|
|
Actually, she gave us a bunch of formulas:
Reciprocal identities, Tangent and Cotangenet identities, Pythagorean identites, Cofunction identites, and Negative Angle identities.
Do I need to type these out? That's OK, if so. There are like 14 different formulas to choose from. Which one are thinkging of using?
And I need to use a different formula for each part of the problem, right? So, for this one wouldn't I need to pick 3 of these?
|
|
|
Uber Member
|
|
Oct 7, 2009, 08:59 AM
|
|
Yes. Ok, here I go!
You know that
So,
Isn't that in your list of formulae? :) Well, it's in mine.
|
|
|
New Member
|
|
Oct 7, 2009, 09:05 AM
|
|
Yes :) Those are in my list.
So, Can I set it up like this:
Sin^2Theta+Cos^2Theta=1+1+Tan^2Theta=Sec^2Theta?
I don't think I did that right though, it looks weird XD
|
|
|
Uber Member
|
|
Oct 7, 2009, 09:07 AM
|
|
No, you cannot put all of them on a line. The way you put it means:
which is false!
You can however write:
|
|
|
New Member
|
|
Oct 7, 2009, 09:48 AM
|
|
So, I don't need to use a separate formula for each part of the identity? The sin, cos, and tan?
Is this how your saying you set it up?
Sin^2Theta+Tan^2Theta+Cos^2Theta=Sec^2Theta
1+Tan^2Theta=Sec^2Theta
Then, simpifly from there?
|
|
|
Uber Member
|
|
Oct 7, 2009, 09:51 AM
|
|
Well, that's how I would have done it... since tan^2theta + 1 = sec^2theta
|
|
|
New Member
|
|
Oct 7, 2009, 09:56 AM
|
|
Oh, OK I thought so :) Thanks so much for the help!
I was looking at the other formulas and I don't think it can be simpifed anymore, can it? Because I don't see anymore that have tan and sec.
So, that would make tan^2theta + 1 = sec^2theta the answer, correct?
|
|
|
Uber Member
|
|
Oct 7, 2009, 10:11 AM
|
|
Yes :)
|
|
|
New Member
|
|
Oct 7, 2009, 11:26 AM
|
|
Ok. Thank you VERY much for taking time out of your day to help me!
|
|
|
Uber Member
|
|
Oct 7, 2009, 11:33 AM
|
|
You're welcome! :)
|
|
Question Tools |
Search this Question |
|
|
Check out some similar questions!
Trig Identities
[ 1 Answers ]
Solve each trig. Equation for x in interval 0 < x < 360
a) 8sin^2x - 8sinx + 1 = 0
b) sin(x + 360/4) = (squared 2) cos x
Trig identities
[ 6 Answers ]
I am supposed to use the double-angle identitie for this one and solve sin(x) to equal 2sin(x), I no the answer but it's the process I don't get.. can anyone help?
Trig identities
[ 1 Answers ]
can you please fully write out the answer to verifying the trig identity sec2x- cos2x / sin2x - sinx * cosx= 1+ tanx?
Trig identities
[ 1 Answers ]
How do you prove that (1 - cos2x)/sin2x = tanx?
View more questions
Search
|