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If anyone is REALLY bored tonight (Trig Question)Follow

#1 Oct 31 2007 at 7:18 PM Rating: Good
I have an exam tomorrow and I wanted to make sure I was on track with a specific problem that was giving me troubles.

cot²Θ
1-cscΘ

It is supposed to be simplified until there is only one trig function left but I'm unable to do so. This is my work thus far:

cot²Θ/1-cscΘ

(cos²Θ/sin²Θ)/1-(1/sinΘ)

(cos²Θ/sin²Θ) * (1 - sinΘ) *this is where I start to be unsure of what needs to happen*

(cos²Θ * (1 - sinΘ)) / sin²Θ *pretty much stuck here


Any thoughts? This is really the only problem that I've been stumped on for this review, so I'm not terribly worried about not figuring this out but if anyone had any input I'd be grateful.

#2 Oct 31 2007 at 7:30 PM Rating: Good
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Wint wrote:
I have an exam tomorrow and I wanted to make sure I was on track with a specific problem that was giving me troubles.

cot²Θ
1-cscΘ

It is supposed to be simplified until there is only one trig function left but I'm unable to do so. This is my work thus far:

(cos²Θ/sin²Θ) * (1 - sinΘ) *this is where I start to be unsure of what needs to happen*

(cos²Θ * (1 - sinΘ)) / sin²Θ *pretty much stuck here


Any thoughts? This is really the only problem that I've been stumped on for this review, so I'm not terribly worried about not figuring this out but if anyone had any input I'd be grateful.

I'll use x since I'm too lazy to type theta.

cot^2x/1-cscx

(1-csc^2x)/1-cscx
(1+cscx)(1-cscx)/1-cscx
1+cscx

I'm a bit rusty on trig identities, but is that what you have to do?



Edited, Oct 31st 2007 10:31pm by sweetumssama
#3 Oct 31 2007 at 7:32 PM Rating: Good
sweetumssama wrote:
1+cscx

I'm a bit rusty on trig identities, but is that what you have to do?


Yes this is perfect. I always forget to break things out into factors Smiley: banghead
#4 Oct 31 2007 at 7:34 PM Rating: Decent
Wtf is this ****?
#5 Oct 31 2007 at 7:37 PM Rating: Decent
LobsterJohnson the Sly wrote:
Wtf is this sh*t?


It's the language of the aliens. They're taking over, dude.
#6 Oct 31 2007 at 7:37 PM Rating: Decent
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Quote:
Wtf is this sh*t?


smart people math.
#7 Oct 31 2007 at 7:43 PM Rating: Good
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Sweetumssama wrote:
I'll use x since I'm too lazy to type theta.

cot^2x/1-cscx

(1-csc^2x)/1-cscx
(1+cscx)(1-cscx)/1-cscx
1+cscx

I'm a bit rusty on trig identities, but is that what you have to do?


I'm not sure on this, but since the exponent is on the inside of the parantheses, (1-cos²Θ), it can't be factored like (1-cosΘ)² can be. But it's been a few years since I've had trig, so I may be missing some rules.

Edited, Oct 31st 2007 11:50pm by Mase
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#8 Oct 31 2007 at 7:44 PM Rating: Good
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Mase wrote:
Sweetumssama wrote:
I'll use x since I'm too lazy to type theta.

cot^2x/1-cscx

(1-csc^2x)/1-cscx
(1+cscx)(1-cscx)/1-cscx
1+cscx

I'm a bit rusty on trig identities, but is that what you have to do?


I'm not sure on this, but since the exponent is on the inside of the parantheses, (1-cos²Θ), it can't be factored like (1-cosΘ)² can be. But it's been a few years since I've had trig, so I may be missing some rules.

cos^2x is just like x^2 (in terms of factoring, anyway), and it's a difference of two squares.

Edited, Oct 31st 2007 10:44pm by sweetumssama
#9 Oct 31 2007 at 7:45 PM Rating: Decent
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Just to make it clear, it took me 5 years to pass algebra 1. Now when it come to Lit., History, and Music Theroy I am good to go.



Edit to add comas. And spelling.
Edited, Oct 31st 2007 10:47pm by jackjeckel

Edited, Oct 31st 2007 10:48pm by jackjeckel
#10 Oct 31 2007 at 7:46 PM Rating: Decent
jackjeckel the Pest wrote:
Just to make it clear, it took my 5 years to pass algebra 1. Now whe it come to Lit. History and Music Theroy I am good to go.
SERIOUSLY
#11 Oct 31 2007 at 7:46 PM Rating: Good
jackjeckel the Pest wrote:
Just to make it clear, it took my 5 years to pass algebra 1. Now whe it come to Lit. History and Music Theroy I am good to go.


I'll cover the sciences.
#12 Oct 31 2007 at 7:47 PM Rating: Decent
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4,618 posts
LobsterJohnson the Sly wrote:
jackjeckel the Pest wrote:
Just to make it clear, it took my 5 years to pass algebra 1. Now whe it come to Lit. History and Music Theroy I am good to go.
SERIOUSLY

SERIOUSLY!!
#13 Oct 31 2007 at 7:49 PM Rating: Good
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Sweetumssama wrote:
cos^2x is just like x^2 (in terms of factoring, anyway), and it's a difference of two squares.


Oh yeah, you're right.
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#14 Oct 31 2007 at 7:52 PM Rating: Good
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It took me a little different route, but I too came up with the 1-csc(x).

If you want, I can post the method I used.
#15 Oct 31 2007 at 7:54 PM Rating: Good
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Mase wrote:


Edit: Also, the Pythagorean ID is cot²Θ = csc²Θ - 1. Not 1 - csc²Θ. So that makes a bit of a difference too.
Yea, I get them mixed up a lot. :S

cot^2x/1-cscx
(csc^2x-1)/1-cscx
(cscx-1)(cscx+1)/1-cscx
-1(1-cscx)(cscx-1)/1-cscx
-1(cscx-1)
1-cscx

So, now without the mixup.

Edit: I always mess up on negatives, god damn it.

Edited, Oct 31st 2007 11:28pm by sweetumssama
#16 Oct 31 2007 at 8:02 PM Rating: Good
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OVERUSED MATH IDENTITY INCOMING (because I actually used this in my Discrete Math class last week):

x = .99999999...
10x = 9.9999999...

10x - x = 9x = 9

x = 1 = .99999999...
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#17 Oct 31 2007 at 8:14 PM Rating: Decent
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God I hated Trig. I'm so glad I'll never have to do it again.
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#18 Oct 31 2007 at 8:18 PM Rating: Decent
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Shenanigians.
#19 Oct 31 2007 at 10:50 PM Rating: Good
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This is what I got:

 
cot^2 x 
--------- = 
1 - csc x 
 
csc^2 x - 1 
----------- =            (From 1 + cot^2 = csc^2) 
1 - csc x 
 
(csc x + 1)(csc x - 1) 
---------------------- = (Dif of perfect squares) 
           (1 - csc x) 
 
(csc x + 1)(-1) = 
 
-csc x - 1 
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#20 Nov 01 2007 at 2:39 AM Rating: Good
Thanks for all of the constructive replies Smiley: smile I put some extra emphasis on studying my pythagorean identities last night, he usually only uses sin²x + cos²x = 1 but on this one he decided to break with tradition I guess.
#21 Nov 01 2007 at 3:27 AM Rating: Good
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Quote:
x = .99999999...
10x = 9.9999999...

10x - x = 9x = 9

x = 1 = .99999999...




10x = 9.999999(...)90
x = .999999(...)9
10x - x = 9x
9.99999(...)90 - .999999(...)9 = 8.999999(...)91
9x = 8.999999(...)91
x times 9 = 8.999999(...)91


And everything fits neatly together like it should!
#22 Nov 01 2007 at 5:10 AM Rating: Good
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Wint wrote:
Thanks for all of the constructive replies Smiley: smile I put some extra emphasis on studying my pythagorean identities last night, he usually only uses sin²x + cos²x = 1 but on this one he decided to break with tradition I guess.
Just remember the main one and derive whichever one you need from it, to me it was much easier than remembering several of them.
#23 Nov 01 2007 at 5:20 AM Rating: Decent
Unless you need it for your profession, learning how to do math that DOESN'T involve your fingers seems excessive IMO. Just sayin.
#24 Nov 01 2007 at 6:45 AM Rating: Good
That test sucked. He claimed it was easier than the review sheet, but there was at least one problem on there I had no idea how to answer. We were supposed to graph a function and given certain points on it we had to rewrite it in the form y=Asin(Bx+C) + D. I figured out the period, the amplitude, and the baseline, but I couldn't get the phase shift worked out for the life of me. Since we also had to prove that it equaled the original equation, I'm pretty sure I lost all 10 points on that one. Smiley: banghead
#25 Nov 01 2007 at 6:52 AM Rating: Decent
jklotros wrote:
Unless you need it for your profession, learning how to do math that DOESN'T involve your fingers seems excessive IMO. Just sayin.


Quote:

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[cutaway to Chris asking a man for directions]
Man: Okay, now what you gotta do is go down the road past the old Johnson place, then you're gonna find two roads; one parallel and one perpendicular. Now keep going until you come to a highway that bisects it at a 45-degree angle. Solve for X. [camera pulls back to show Chris in the fetal position sucking his thumb] Peter Griffin: [chuckling] Math! Math my dear boy is but the lesbian sister of Biology.




#26 Nov 01 2007 at 7:26 AM Rating: Good
Wint wrote:
That test sucked. He claimed it was easier than the review sheet, but there was at least one problem on there I had no idea how to answer. We were supposed to graph a function and given certain points on it we had to rewrite it in the form y=Asin(Bx+C) + D. I figured out the period, the amplitude, and the baseline, but I couldn't get the phase shift worked out for the life of me. Since we also had to prove that it equaled the original equation, I'm pretty sure I lost all 10 points on that one. Smiley: banghead


Wow.. I can tell I haven't taken trig in 10 yrs (/cry)... Good luck though. Hopefully you'll do decent.
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